Measurement devices and methods for measuring analyte concentration incorporating temperature and ph correction

ABSTRACT

Disclosed herein are methods of estimating an analyte concentration which include generating a signal indicative of the analyte concentration, generating a signal indicative of a temperature, generating a signal indicative of a pH, and transforming the signal indicative of the analyte concentration utilizing an equation of the form of a modified Michaelis-Menten equation depending on Michaelis-Menten parameters, wherein values of the Michaelis-Menten parameters are set based upon data which includes temperature and pH calibration parameters, the signal indicative of a temperature, and the signal indicative of a pH. Also disclosed herein are measurement devices which employ the aforementioned methods.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is related to co-pending U.S. patent application Ser.No. 12/794,466, filed Jun. 4, 2010, the disclosure of which is herebyexpressly incorporated by reference in its entirety and is herebyexpressly made a portion of this application.

INCORPORATION BY REFERENCE TO ANY PRIORITY APPLICATIONS

Any and all applications for which a foreign or domestic priority claimis identified in the Application Data Sheet as filed with the presentapplication are hereby incorporated by reference under 37 CFR 1.57.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present application discloses embodiments which relate to the fieldof analyte concentration measurement, more specifically, glucoseconcentration measurement, and, in some embodiments, algorithms andmethods of temperature and/or pH correction, and measurement deviceswhich perform temperature and/or pH correction.

2. Description of the Related Art

Types 1 and 2 diabetes are endocrine disorders characterized byabnormalities in the body's ability to regulate glucose metabolism.While the underlying pathology of these two illnesses differ, both areassociated with significant complications including diabeticnephropathy, neuropathy, retinopathy, problems with wound healing, aswell as an elevated risk of cerebrovascular and cardiovascular disease.While the mechanism of action is uncertain, it is believed that elevatedglucose levels are associated with the release of various inflammatorymediators that produce vascular damage ultimately leading to thesecomplications. Abnormally low glucose levels can also be problematicresulting in anxiety, weakness, and in extreme cases coma and death.Researchers and clinicians have increasingly become aware of theimportance of maintaining tight control of glucose levels, particularlyin acute care settings, so as to prevent these complications fromoccurring and to facilitate patient recovery.

While clinicians have used insulin for decades to regulate glucoselevels in diabetics, determining precise dosages remains a problem.Insulin has the overall effect of reducing circulating glucose levelsthrough a series of complex interactions involving a number of hormonesand cell types. While dosage protocols for insulin attempt to replicatethe physiologic secretion of the hormone by the pancreas, administeringaccording to fixed times and algorithms based on serum glucosemeasurements can only crudely approximate the ability of a healthyindividual to continuously adjust insulin production in response toglucose levels and the needs of the body. It follows that in order todetermine the precise amount of insulin that must be administered tomaintain a patient's circulating glucose levels at a normal level, it isnecessary to have an extremely accurate measurement of how much glucoseis present and available to the patient at any given time.

Unfortunately, existing methods of determining a patient's glucose levelleave much to be desired. Clinicians and diabetic patients routinelytest glucose levels by testing unprocessed blood. While the results canbe available quickly, they can often be inaccurate. Glucose freelydiffuses in and out of red blood cells which can cause the result tovary depending on the concentration of such cells in the sample.Furthermore, the diffusion of glucose out of blood cells is oftenmagnified by the requirement that the whole blood be diluted, thusaltering the osmotic potential across the membranes of the blood cells.

A more accurate determination of the patient's glucose level can beobtained by measuring plasma glucose. This requires the separation ofthe plasma from the other components of the blood such as red and whiteblood cells. There exist a number of analytical methods for measuringplasma glucose concentration. These include the measurement of thecurrent produced by glucose oxidation, the use of the hexokinasereaction, or through the use of mass spectrometry. While the latterrepresents the “gold standard” for glucose measurement, these methodscan be technically complicated, time-consuming, and are frequently notcost-effective for clinical use. For example, for the most accuratereadings, lipids should be removed from the plasma and the resultsshould be adjusted for the sodium content, but both are rarely done.Finally, the results can vary depending on how much protein-bound andintercellular glucose has been released into the sample prior to andduring processing. While plasma glucose measurements can providerelatively accurate information, transportation and processing times canlead to a significant delay between when the sample is collected andwhen the results are available to the clinician. Therefore, it is notfeasible to use plasma glucose measurements for near-instantaneous, or“real-time” monitoring of a patient's glucose level.

SUMMARY OF THE INVENTION

Disclosed herein are methods of estimating an analyte concentrationwhich may include generating a signal indicative of the analyteconcentration, generating a signal indicative of a temperature, andtransforming the signal indicative of the analyte concentrationutilizing an equation of the form of a modified Michaelis-Mentenequation depending on Michaelis-Menten parameters, wherein values of theMichaelis-Menten parameters are set based on data which may includetemperature calibration data and the signal indicative of a temperature.

Also disclosed herein are methods of estimating an analyte concentrationwhich may include generating a signal indicative of the analyteconcentration, generating a signal indicative of a temperature, andtransforming the signal indicative of the analyte concentrationutilizing an equation of the form of a modified Michaelis-Mentenequation wherein at least one of the Michaelis-Menten parameters hasbeen substituted with a calibration equation functionally depending on aset of one or more temperature calibration parameters and the signalindicative of temperature.

Also disclosed herein are methods of estimating an analyte concentrationwhich may include generating a signal indicative of the analyteconcentration, generating a signal indicative of a pH, and transformingthe signal indicative of the analyte concentration utilizing an equationof the form of a modified Michaelis-Menten equation depending onMichaelis-Menten parameters, wherein values of the Michaelis-Mentenparameters are set based on data which may include pH calibration data,and the signal indicative of a pH.

Also disclosed herein are methods of estimating an analyte concentrationwhich may include generating a signal indicative of the analyteconcentration, generating a signal indicative of a pH, and transformingthe signal indicative of the analyte concentration utilizing an equationof the form of a modified Michaelis-Menten equation wherein at least oneof the Michaelis-Menten parameters has been substituted with acalibration equation functionally depending on a set of one or more pHcalibration parameters and the signal indicative of pH.

Also disclosed herein are methods of estimating an analyte concentrationwhich may include generating a signal indicative of the analyteconcentration, generating a signal indicative of a temperature,generating a signal indicative of a pH, and transforming the signalindicative of the analyte concentration utilizing an equation of theform of a modified Michaelis-Menten equation depending onMichaelis-Menten parameters, wherein values of the Michaelis-Mentenparameters are set based on data which may include temperature and pHcalibration parameters, the signal indicative of a temperature, and thesignal indicative of a pH.

Also disclosed herein are methods of estimating an analyte concentrationof a solution which may include generating a signal indicative of theanalyte concentration of the solution, generating a signal indicative ofa temperature of the solution, generating a signal indicative of a pH ofthe solution, and transforming the signal indicative of the analyteconcentration utilizing an equation of the form of a modifiedMichaelis-Menten equation wherein at least one of the Michaelis-Mentenparameters has been substituted with a calibration equation functionallydepending on a set of one or more temperature and pH calibrationparameters, the signal indicative of the temperature, and the signalindicative of the pH.

Also disclosed herein are measurement devices for estimating an analyteconcentration of a sample. In some embodiments, the measurement devicesmay include an analyte sensing element, a temperature sensing element,and a receiving and processing unit. In some embodiments, the analytesensing element may be configured to generate a first signal, the firstsignal indicative of the analyte concentration of the sample. In someembodiments, the temperature sensing element may be configured togenerate a second signal, the second signal indicative of a temperatureof the sample. In some embodiments, the receiving and processing unitmay be configured to transform the first signal utilizing an equation ofthe form of a modified Michaelis-Menten equation depending onMichaelis-Menten parameters, wherein values of the Michaelis-Mentenparameters are set based upon data which may include temperaturecalibration data, and the second signal.

The measurement devices for estimating an analyte concentration of asample may, in some embodiments, include an analyte sensing element, apH sensing element, and a receiving and processing unit. In someembodiments, the analyte sensing element may be configured to generate afirst signal, the first signal indicative of the analyte concentrationof the sample. In some embodiments, the pH sensing element may beconfigured to generate a second signal, the second signal indicative ofa pH of the sample. In some embodiments, the receiving and processingunit may be configured to transform the first signal utilizing anequation of the form of a modified Michaelis-Menten equation dependingupon Michaelis-Menten parameters, wherein values of the Michaelis-Mentenparameters are set based on data which may include pH calibration data,and the second signal.

The measurement devices for estimating an analyte concentration of asample, may, in some embodiments, include an analyte sensing element, atemperature sensing element, and a pH sensing element. In someembodiments, the analyte sensing element may be configured to generate afirst signal, the first signal indicative of the analyte concentrationof the sample. In some embodiments, the temperature sensing element maybe configured to generate a second signal, the second signal indicativeof a temperature of the sample. In some embodiments, the pH sensingelement may be configured to generate a third signal, the third signalindicative of a pH of the sample. In some embodiments, the receiving andprocessing unit may be configured to transform the first signalutilizing an equation of the form of a modified Michaelis-Mentenequation depending on Michaelis-Menten parameters, wherein values of theMichaelis-Menten parameters are set based upon data which may includetemperature and pH calibration data, the second signal, and the thirdsignal.

The measurement devices for estimating an analyte concentration of asample, may, in some embodiments, include an analyte and pH sensingelement, and a receiving and processing unit. In some embodiments, theanalyte and pH sensing element may be configured to generate a firstsignal, the first signal indicative of the analyte concentration of thesample and a pH of the sample. In some embodiments, the analyte and pHsensing element may be configured to generate a second signal, thesecond signal indicative of the analyte concentration of the sample andthe pH of the sample. In some embodiments, the receiving and processingunit may be configured to transform a third signal utilizing an equationof the form of a modified Michaelis-Menten equation depending onMichaelis-Menten parameters, wherein values of the Michaelis-Mentenparameters are set based upon data which may include pH calibration dataand a fourth signal. In some embodiments, the third signal may beindicative of the analyte concentration and may be generated based upondata which may include the first signal and the second signal. In someembodiments, the fourth signal may be indicative of the pH and may begenerated based upon data which may include the first signal and thesecond signal.

The measurement devices for estimating an analyte concentration of asample may, in some embodiments, include an analyte and pH sensingelement, a temperature sensing element, and a receiving and processingunit. In some embodiments, the analyte and pH sensing element may beconfigured to generate a first signal, the first signal indicative ofthe analyte concentration of the sample and a pH of the sample, and asecond signal, the second signal indicative of the analyte concentrationof the sample and the pH of the sample. In some embodiments, thetemperature sensing element may be configured to generate a thirdsignal, the third signal indicative of a temperature of the sample. Insome embodiments, the receiving and processing unit may be configured totransform a fourth signal utilizing an equation of the form of amodified Michaelis-Menten equation depending on Michaelis-Mentenparameters, wherein values of the Michaelis-Menten parameters are setbased upon data which may include temperature and pH calibration data,the third signal, and a fifth signal. In some embodiments, the fourthsignal may be indicative of the analyte concentration and may begenerated based upon data which may include the first signal and thesecond signal. In some embodiments, the fifth signal may be indicativeof the pH and may be generated based upon data which may include thefirst signal and the second signal.

Also disclosed herein are methods of estimating an analyte concentrationfrom a signal indicative of the analyte concentration. In someembodiments, the methods may include transforming the signal using anequation of the form of a modified Michaelis-Menten equation wherein thevalues of one or more Michaelis-Menten parameters have been adjusted fortemperature. In some embodiments, the values of one or moreMichaelis-Menten parameters may also have been adjusted for pH.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A is a flow chart schematically illustrating the sensing mechanismof one embodiment of the present invention which includes a temperaturesensing element and an analyte sensing element.

FIG. 1B is a flow chart schematically illustrating the sensing mechanismof one embodiment of the present invention which includes an analytesensing element and a pH sensing element.

FIG. 1C is a flow chart schematically illustrating the sensing mechanismof one embodiment of the present invention which includes a pH andanalyte sensing element.

FIG. 1D is a flow chart schematically illustrating the sensing mechanismof one embodiment of the present invention which includes a temperaturesensing element, an analyte sensing element, and a pH sensing element.

FIG. 1E is a flow chart schematically illustrating the sensing mechanismof one embodiment of the present invention which includes a temperaturesensing element and a pH and analyte sensing element.

FIG. 2A schematically illustrates a dual light source, dual detectormeasurement device in accordance with certain embodiments disclosedherein.

FIG. 2B schematically illustrates a dual light source measurement deviceincorporating a microspectrometer and/or spectrometer in accordance withcertain embodiments disclosed herein.

FIG. 2C schematically illustrates a dual light source, dual detectormeasurement system incorporating a beam splitter in accordance withcertain embodiments disclosed herein.

FIG. 3 is a cut-away view of a sensor probe wherein a portion of theporous membrane sheath is cut away to expose the optical fiber andhydrogel beneath the membrane.

FIG. 4 is a cross-sectional view along a longitudinal axis of a sensorprobe with a hydrogel disposed in the sensor probe distal to the opticalfiber.

FIG. 5A shows a sensor probe having a series of holes that form ahelical configuration.

FIG. 5B shows a sensor probe having a series of holes drilled or formedat an angle.

FIG. 5C shows a sensor probe having at least one spiral groove.

FIG. 5D shows a sensor probe having a series of triangular wedgecut-outs.

FIG. 6 shows a cross-sectional view of one embodiment of a sensor probehaving a cavity in the distal portion of the sensor probe.

FIG. 7A shows a sensor probe with a protective housing surrounding anindicator system, the protective housing including a tubular meshsurrounded by a polymeric material with an open window leading to theindicator system.

FIG. 7B shows a sensor probe with a protective housing surrounding anindicator system, the protective housing including a coil surrounded bya polymeric material with an open window leading to the indicatorsystem.

FIG. 8 displays four plots of fluorescent signal versus glucoseconcentration at four different temperatures generated by one embodimentof a measurement device disclosed herein.

FIG. 9 displays the four plots of FIG. 8 with each constant temperatureplot normalized to the value of its fluorescent signal at 50 mg/dL.

FIG. 10 displays essentially the same raw data as FIG. 8, but insteaddisplays four plots of fluorescent signal versus temperature at fourdifferent glucose concentrations.

FIG. 11 displays the fluorescent signal generated by one embodiment ofan analyte measuring device disclosed herein at four temperatures andfour glucose concentrations.

FIG. 12 displays a plot of fluorescent signal versus glucoseconcentration at four temperatures as generated by one embodiment of ananalyte measuring device disclosed herein.

FIG. 13 displays plots of the values of the three Michaelis-Mentenparameters versus temperature.

FIG. 14 displays plots of normalized values of the threeMichaelis-Menten parameters versus temperature and displays a best fitline associated with each normalized parameter.

FIG. 15 compares a plot of glucose concentration as determined byreference measurements with a plot of glucose concentration asdetermined by one embodiment of an analyte measuring device disclosedherein.

FIG. 16 displays plots of the ratio of two fluorescent signals versus pHat four glucose concentrations.

FIG. 17 displays plots of two fluorescent signals at four temperaturesand four pH levels.

FIG. 18 displays plots of two fluorescent signals at four temperaturesand four pH levels.

FIG. 19 displays plots of the ratio of two fluorescent signals versus pHat four temperatures, along with best fit lines corresponding to eachtemperature.

FIG. 20 displays plots of the slopes and intercepts of the best fitlines of FIG. 19 at each of the temperatures from that figure.

FIG. 21 compares a plot of pH as determined by reference measurementswith a plot of pH as determined by one embodiment of an analytemeasuring device disclosed herein.

FIG. 22 displays plots of two fluorescent signals at five pH levels andfour glucose concentrations.

FIG. 23 displays plots of fluorescent signal versus glucoseconcentration at five pH levels.

FIG. 24 displays plots of the values of the three Michaelis-Mentenparameters versus pH.

FIG. 25 displays plots of normalized values of the threeMichaelis-Menten parameters versus pH.

FIG. 26 compares a plot of glucose concentration as determined byreference measurements with a plot of glucose concentration asdetermined by one embodiment of an analyte measuring device (“GluCath”)disclosed herein.

FIG. 27 displays a magnified portion of the plots of FIG. 26.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

Whole blood glucose activity is a physiologically significant quantitythat may be used to determine proper insulin dosage. Glucose activityrepresents an estimate of the concentration of bioavailable (or free)glucose in water, blood, or any solution. Hence, a patient's whole bloodglucose activity level is a physiologically more appropriate quantity bywhich to estimate insulin dosage, than estimated total blood glucoseconcentration as determined by the various methods mentioned above.Typically, glucose activity is measured through the establishment of areversible, equilibrium-based, affinity-driven binding interactionbetween glucose and some moiety capable of binding free glucose. Glucoseactivity is not substantially affected by the presence of red bloodcells, protein or lipid concentration, nor oxygenation levels.Accordingly, the time consuming step of extracting plasma from wholeblood is not required, and glucose activity measurements can be madeavailable in near “real-time.” Furthermore, since glucose activity canbe measured on whole blood without dilution, it provides an estimate ofbioavailable glucose not polluted by the effects of altering away frombiological norms, the osmotic potentials across blood cell membranes.

Fluorescent techniques may be used to efficiently and accurately measurethe concentration of glucose (and other polyhydroxyl compounds).Oftentimes, these techniques may also be used to measure theconcentration of bioavailable glucose in whole blood, i.e. the glucoseactivity of whole blood. For instance, several attempts have been madeto detect glucose by fluorescence using dyes associated with boronicacid groups. Boronate moieties bind glucose reversibly. When boronicacid functionalized fluorescent dyes bind glucose, the properties of thedye are affected, such that a signal related to the concentration ofglucose may be generated and detected. For example, Russell (U.S. Pat.Nos. 5,137,833 and 5,512,246) used a boronic acid functionalized dyethat bound glucose and generated a signal related to the glucoseconcentration. James et al. (U.S. Pat. No. 5,503,770) employed a similarprinciple, but combined a fluorescent dye, an amine quenchingfunctionality, and boronic acid in a single complex. The fluorescenceemission from the complex varied with the amount of glucose binding. VanAntwerp et al. (U.S. Pat. Nos. 6,002,954 and 6,011,984) combinedfeatures of the previously cited references and also disclosed a devicepurported to be implantable. A. E. Colvin, Jr. (U.S. Pat. No. 6,304,766)also disclosed optical-based sensing devices for in situ sensing inhumans that utilize boronate-functionalized dyes. Suri (U.S. Pat. No.7,417,164) recently disclosed several fluorescent dyes capable of beingused to estimate glucose concentration or activity.

Measurement Devices

Various embodiments of the measurement devices disclosed herein comprisean analyte sensing element configured to generate a signal indicative ofthe analyte concentration of a sample. The analyte sensing element mayinclude at least one light source, an indicator system, and at least onedetector. In some embodiments, the indicator system (described morefully below) may include at least one type of fluorophore and at leastone type of binding moiety. In some embodiments, the fluorophore emits afluorescence having an intensity in response to light from the at leastone light source. In some embodiments, the binding moiety is capable ofbinding the analyte and is operably coupled to the fluorophore, suchthat when the sample contacts the binding moiety the intensity isindicative of the concentration of the analyte. In one embodiment, thebinding moiety acts as a quencher in the presence of the analyte suchthat when the binding moiety binds the analyte it interacts with thefluorophore in such a manner as to quench or reduce the fluorescentemission intensity. In preferred embodiments, the binding moietyassociates with the fluorophore in the absence of the analyte therebyquenching the fluorescent emission intensity. Analyte binding by thebinding moiety causes disassociation from the fluorophore, such that thefluorescent emission intensity increases with increasing concentrationof analyte. In some embodiments, the analyte sensing element includes atleast one detector which may be configured to detect the intensity andgenerate a signal indicative of the analyte concentration in response tothe intensity.

Examples of glucose-sensing chemical indicator systems and glucosesensor configurations for intravascular glucose monitoring include theoptical sensors disclosed in U.S. Pat. Nos. 5,137,033, 5,512,246,5,503,770, 6,627,177, 7,417,164 and 7,470,420, and U.S. Patent Publ.Nos. 2008/0188722, 2008/0188725, 2008/0187655, 2008/0305009,2009/0018426, 2009/0018418, and co-pending U.S. patent application Ser.Nos. 11/296,898, 12/187,248, 12/172,059, 12/274,617, 12/424,902 and61/184,747; each of which is incorporated herein in its entirety byreference thereto.

In some embodiments, the concentration being estimated corresponds tothe glucose activity of a sample. In some embodiments, the sample iswhole blood. However, the embodiments disclosed herein may also measurethe concentrations and/or activities of other analytes. For instance,disclosed measurement devices may, in some embodiments, be configured tomeasure the concentrations of other polyhydroxyl-containing organiccompounds including, but not limited to, carbohydrates, 1,2-diols,1,3-diols and the like. In some embodiments, the analytes to be measuredmay include non-carbohydrates. Generally, the measurement devicesdisclosed herein may be configured to estimate the concentration of anyanalyte which may be bound by a binding moiety, wherein the bindingmoiety is operably coupled to a fluorophore which emits a fluorescenceindicative of the concentration of the analyte after being excited bylight of the appropriate wavelength and intensity. The discussion of themeasurement devices that follows will usually refer to the physicalquantity to be measured as an “analyte concentration” or simply a“concentration.” However, it is to be understood that “concentration” asused below refers to both “analyte concentration” as that phrase wouldbe ordinarily used and also to “activity” (in some cases “glucoseactivity”) as that phrase is described above.

Various measurement devices disclosed herein are configured to provideimproved estimates of the analyte concentration of a particular solutionby taking the temperature and/or the pH of the particular solution intoaccount. Accordingly, some embodiments of the measurement devicesdisclosed herein may include a temperature sensing element configured togenerate a signal indicative of a temperature of the sample. Likewise,some embodiments of the measurement devices disclosed herein may includea pH sensing element configured to a signal indicative of a pH of thesample. Moreover, some embodiments disclosed herein may include both atemperature sensing element and a pH sensing element,

In some embodiments disclosed herein, a single element may be configuredto sense both pH and analyte concentration. In certain embodiments, thisanalyte and pH sensing element may be configured to generate twosignals, both of which are indicative of analyte concentration and pH.Thus, in certain embodiments, an analyte and pH sensing element maygenerate a first signal indicative of an analyte concentration of asample and a pH of the sample, and also generate a second signalindicative of the analyte concentration of the sample and the pH of thesample. Moreover, some embodiments including an analyte and pH sensingelement may further include a temperature sensing element configured togenerate a third signal which is indicative of a temperature of thesample.

In certain embodiments, the measurement devices disclosed herein mayfurther include a receiving and processing unit. In some embodiments,the receiving and processing unity may be configured to transform asignal indicative of analyte concentration, which has been generated byan analyte sensing element. In some embodiments, the receiving andprocessing unit may transform the signal utilizing an equation of theform of a modified Michaelis-Menten equation depending onMichaelis-Menten parameters, as described in detail below. In someembodiments, the values of the Michaelis-Menten parameters may be setbased upon data which may include temperature calibration data and asignal indicative of temperature which has been generated by atemperature sensing element. In some embodiments, the values of theMichaelis-Menten parameters may be set based upon data which may includepH calibration data and a signal indicative of pH which has beengenerated by a pH sensing element. In some embodiments, the values ofthe Michaelis-Menten parameters may be set based upon data which mayinclude temperature and pH calibration data, a signal indicative oftemperature which has been generated by a temperature sensing element,and a signal indicative of pH which has been generated by a pH sensingelement. In some embodiments, the signal indicative of analyteconcentration—which is transformed by the receiving and processingunit—has been generated based upon data comprising two signals, each ofwhich was generated by an analyte and pH sensing element, and each ofwhich is indicative of analyte concentration and pH. These two signalsmay also be utilized to generate a signal indicative of pH which may beused with calibration data to set values of the Michaelis-Mentenparameters.

FIGS. 1A through 1E are flow charts illustrating the sensing mechanismcorresponding to some embodiments of the measurement devices 100disclosed herein. These flow charts may correspond to the sensingmechanism of an in vitro measurement device for use on the laboratorybench top, or they may correspond to the sensing mechanism of a deviceused for in vivo analyte sensing. As schematically illustrated in FIG.1A, some embodiments of the measurement devices disclosed herein includeat least one analyte sensing element 105, and may include at least onetemperature sensing element 120. Other configurations of measurementdevices, differing from the configuration illustrated in FIG. 1A, areschematically illustrated in FIGS. 1B through 1E. FIG. 1B, for instance,schematically illustrates a measurement device 100 having an analytesensing element 105 and a pH sensing element 121, but lacking thetemperature sensing element 120 of the configuration illustrated in FIG.1A. FIG. 1C schematically illustrates a measurement device 100 having acombination analyte and pH sensing element 110, instead of the distinctanalyte and pH sensing elements as shown in FIG. 1B. FIG. 1Dschematically illustrates a configuration having an analyte sensingelement 105, a temperature sensing element 120, and a pH sensing element121. FIG. 1E schematically illustrates a configuration having thecombination analyte and pH sensing element 110 of FIG. 1C along with atemperature sensing element 120. The analyte sensing element 105 mayinclude at least one light source 111, at least one detector 115, and anindicator system 113. The indicator system 113 includes the sensingmoieties—including at least one fluorophore and at least one bindingmoiety. In some embodiments, when the sensing moieties contact a samplecontaining the analyte of interest, a reversible, equilibrium-based,affinity-driven binding interaction between the analyte and the at leastone binding moiety is established. This binding interaction alters thebinding moiety's relationship with the fluorophore, such that when thefluorophore is excited by light from the at least one light source 111,its fluorescent emission is different depending on the extent to whichanalyte has been bound by the binding moiety. Thus, emission from thefluorophore is indicative of the concentration of analyte in the sample.In some embodiments, emission from the fluorophore may also beindicative of the pH of the sample. If this is the case, fluorescentemissions may be used to determine pH and analyte concentration asdescribed in U.S. application Ser. No. 11/671,880, entitled “OpticalDetermination of pH and Glucose,” filed Feb. 6, 2007, herebyincorporated by reference herein in its entirety. Whether indicative ofanalyte concentration, pH, or both, the fluorescent emission generatedby the fluorophore (and modulated by the binding moiety) is detected bythe detector 115 which generates a signal indicative of the emission(and thus also the analyte concentration and/or the pH) which is passedto the receiving and processing unit 125. The receiving and processingunit 125 is configured to estimate the concentration of the analyte inthe sample based on one or more signals indicative of analyteconcentration—such as the intensities of the fluorescent emissions. Insome embodiments, the receiving and processing unit 125 may be furtherconfigured to generate temperature and/or pH corrected estimates ofanalyte concentration. The receiving and processing unit 125 may correctfor temperature by receiving and taking into account one or more signalsindicative of temperature generated by the temperature sensing element120, as schematically illustrated in FIGS. 1A, 1D, and 1E. The receivingand processing unit 125 may correct for pH by receiving and taking intoaccount one or more signals indicative of pH generated either by the pHsensing element 121, as schematically illustrated in FIGS. 1B and 1D, orby the analyte and pH sensing element 110. The receiving and processingunit 125 may employ various methods and algorithms of adjusting theestimated concentration based on the signal indicative of temperature,or the signal indicative of pH, or both, as described in further detailbelow. Estimated concentrations may be displayed in a display unit 126and/or stored in a storage unit 127, as schematically illustrated inFIGS. 1A through 1E. Depending on the embodiment, any quantity relatedto analyte concentration (such as quantities derived in whole or in partfrom measurements of optical intensity) may be displayed in the displayunit 126 and/or stored in the storage unit 127, including, but notlimited to the measured fluorescent intensities emitted by thefluorophores, the temperature of the sample, and the pH of the sample.In addition, as schematically illustrated in FIGS. 1A through 1E, someembodiments of the measurement device 100 include one or more filters112 located between the light source 111 and indicator system 113,and/or one or more filters 114 located between the indicator system 113and the detector 115. The filter 112 may serve to select particularwavelengths of light for excitation of the fluorophore, while the filter114 may serve to select particular wavelengths of light for detection.Other optical components may also be utilized (that are not shown inFIGS. 1A through 1E) including, but not limited to, mirrors, collimatingand/or focusing lenses, beam splitters, etc. (See, e.g., FIGS. 2A, 2B,and 2C below.)

In some embodiments, the measurement device 100 may include a controllerunit (not shown in FIGS. 1A through 1E) which controls variousoperations of the measurement device 100 including, but not limited to,control of the light sources, control of detectors, and responding tooperator input or actions. The controller unit can be any type known inthe art and capable of controlling the measuring device including, butnot limited to, a microprocessor, an embedded processor, amultiprocessor, a general purpose computer, a special purpose processor,a microcontroller, a programmable gate array or any combination thereof.

Analyte Sensing Elements, pH Sensing Elements, and Analyte and pHSensing Elements

Various measurement devices disclosed herein include an analyte sensingelement or an element capable of sensing both analyte concentration andpH—referred to herein as an analyte and pH sensing element. The latterdual purpose elements are schematically illustrated, for example, inFIGS. 1C and 1E. However, as indicated by FIGS. 1B and 1D, variousembodiments of the measurement devices 100 disclosed herein may includean analyte sensing element 105, and a pH sensing element 121 separatefrom the analyte sensing element 105. When the pH sensing element 121 isdistinct from the analyte sensing element 105, it may consist of any ofa number of standard pH sensing devices which are known in the art solong as the device is properly sized and is capable of generating asignal indicative of pH which exhibits sufficient accuracy and precisionto serve as a basis for applying pH correction to a signal indicative ofanalyte concentration. Of course, in measurement devices 100 that do notimplement pH correction, such as those corresponding to the schematicillustration of FIG. 1A, a pH sensing element is not needed for thispurpose and may be omitted.

An analyte sensing element may be configured to generate a signalindicative of the analyte concentration of a sample and may include atleast one light source, an indicator system, and at least one detector.In some embodiments, the indicator system (described more fully below)may include at least one type of fluorophore and at least one type ofbinding moiety (each described in greater detail below), and in someembodiments, an immobilizing medium whose presence may prevent some ofthe fluorophores and/or some of the binding moieties from freelydiffusing through the sample (as described in greater detail below). Insome embodiments, the fluorophore emits a fluorescence having anintensity in response to light from the at least one light source. Insome embodiments, the binding moiety is capable of binding the analyteand is operably coupled to the fluorophore, such that when the samplecontacts the binding moiety the intensity is indicative of theconcentration of the analyte. In some embodiments, the analyte sensingelement includes at least one detector which may be configured to detectthe intensity and generate a signal indicative of the analyteconcentration of the sample in response to the intensity.

Likewise, a dual purpose, analyte and pH sensing element may beconfigured to generate one or more signals indicative of the analyteconcentration of a sample and the pH of the sample. In some embodiments,an analyte and pH sensing element may include at least one light source,an indicator system, and at least one detector, similarly to the analytesensing elements described in the preceding paragraph. Thus, in someembodiments, the indicator system (described more fully below) mayinclude at least one type of fluorophore and at least one type ofbinding moiety (each described in greater detail below), and in someembodiments, an immobilizing medium whose presence may prevent some ofthe fluorophores and/or some of the binding moieties from freelydiffusing through the sample (as described in greater detail below). Insome embodiments, the fluorophore emits a fluorescence having anintensity in response to light from the at least one light source. Insome embodiments, the binding moiety is capable of binding the analyteand is operably coupled to the fluorophore, such that when the samplecontacts the binding moiety the intensity is indicative of theconcentration of analyte in the sample and the pH of the sample. In someembodiments, the analyte and pH sensing element includes at least onedetector which may be configured to detect the intensity and generateone or more signals indicative of the analyte concentration of thesample and the pH of the sample in response to the intensity.

Some of the measurement devices disclosed herein, only employ a singletype of fluorophore and a single light source. However, it should beunderstood that some embodiments of the measurement devices disclosedherein employ more than one type of fluorophore. Furthermore, someembodiments of measurement devices employing multiple types offluorophores may also employ more than one light source. Similarly,embodiments employing more than one type of fluorophore may also employmore than one detector. In certain such embodiments, the single detectormay be a spectrometer.

However, dual light source and dual detector configurations are notnecessarily limited to configurations utilizing multiple fluorophores,as these dual light source/detector configurations may offer otheradvantages. For instance, a dual light source configuration mightadvantageously allow one light source to serve as a reference for theother, or a dual light source configuration might be useful formeasurement devices employing ratiometric pH determination as disclosedin U.S. Pat. No. 7,751,863, entitled “Optical Determination of pH andGlucose,” which is hereby incorporated herein by reference in itsentirety. Methods and/or algorithms for determining pH based on theratio of two fluorescent emission signals are discussed below, as wellas described in the aforementioned patent. In some embodiments, thesemethods may be implemented in a measurement device employing acombination analyte and pH sensing element which utilizes a dual lightsource configuration, as described below with reference to FIGS. 2Athrough 2C.

Accordingly, embodiments of the measurement devices disclosed herein mayconfigure light sources, detectors, and one or more fluorophores andbinding moieties in a variety of ways. For example, FIG. 2Aschematically illustrates a two light source measurement device inaccordance with certain preferred embodiments of the present invention.With reference to FIG. 2A, the two light sources, 301A and 301B, eachgenerate excitation light. In some embodiments, each of the two lightsources 301A and 301B generates excitation light over a different rangeof wavelengths. In certain such embodiments, the excitation lightgenerated by light source 301A falls within a wavelength rangeappropriate to cause an emission of a first type, and the excitationlight generated by light source 301B falls within a wavelength rangeappropriate to cause an emission of a second type. In some embodiments,the ranges are partially overlapping, while in other embodiments, theranges are fully non-overlapping.

The excitation light generated by light sources 301A and 301B may betransmitted (as illustrated) through collimator lenses 302A and 302B.The collimator lenses 302A and 302B may be aspheric lenses, but othertypes of collimator lenses may also be employed.

In certain embodiments, light exiting from the collimator lenses 302Aand 302B may be transmitted (as illustrated) to interference filters303A and 303B. In some embodiments, each interference filter 303A and303B may attenuate or block a portion of the wavelength ranges generatedby light sources other than the corresponding light source 301A and301B. For instance, in certain such embodiments, interference filter303A may pass light generated by light source 301A, but may severelyattenuate light generated by light source 301B. Interference filter 303Bmay function analogously. In certain embodiments, each interferencefilter 303A and 303B blocks the wavelength range that overlaps with thewavelength range corresponding to emission by the one or more types offluorophores. For example, if a measurement system employs a blueexcitation light to produce a green emission, then an interferencefilter may in some embodiments preferably be used to narrow the band ofblue excitation, because the blue excitation light may comprise bothblue and green light. An unfiltered excitation blue that comprises greenlight can produce inaccurate green emission signal because the greenlight from the excitation light will add to the green emission signal ofthe fluorophore to produce a green light of greater intensity.

The interference filters 303A and 303B can be short or long pass filtersthat block all wavelengths beyond a certain maximum or minimumwavelength. The interference filters 303A and 303B can be band passfilters that only allow a particular band of wavelengths to pass throughthe filters. In certain embodiments, the measurement device employsinterference filters 303A and 303B that are band pass filters because,in certain embodiments, the light sources 301A and 301B generate lightof overlapping wavelength ranges. Thus, the use of non-overlapping bandpass filters 303A and 303B may allow the measurement device to generateexcitation light in distinct bands such that light generated by thelight source 301A selectively creates only excitation of a first type,and light generated by 301B selectively creates only excitation of asecond type. In this manner, in some embodiments, each light source maybe tailored to create a particular type of emission.

In certain embodiments, light exiting from interference filters 303A and303B may be focused (as illustrated) by focusing lenses 304A and 304Binto fiber optic lines 305A and 305B. The fiber optic lines 305A and305B carry the filtered excitation light to the indicator system 307,which is contained within a sensor probe 200. In some embodiments, thesensor probe 200 includes a protective housing 500 which serves toprotect the indicator system 307 contained within the sensor probe 200.In some embodiments, the indicator system is immobilized in animmobilizing medium within the sensor probe 200, as described herein. Insome embodiments, the fiber optic lines 305A and 305B merge into asingle fiber 306 that is continuous with the sensor probe 200. In otherembodiments, the fiber optic lines 305A and 305B remain distinct(although not shown in FIG. 2A). In certain embodiments employing twotypes of fluorophores, the fiber optic lines 305A and 305B may remaindistinct and be configured so as to keep the two types of fluorophoresspatially distinct/separated so that each type of fluorophore may onlyinteract with light traveling to the indicator system down a singleoptical fiber (that is light generated from one of the light sources).In certain other embodiments, the fiber optic lines 305A and 305B may bekept distinct so that one line may be configured so that light travelingdown the line never interacts with any fluorophore—in this mannercreating a reference signal and keeping it free from opticalcontamination by the optically emitting fluorophore interacting withlight travelling down the other fiber optic line. The cross-sections ofthe fibers may vary (as illustrated) from a bundle of fibers surroundinga central optical fiber 306A to a single fiber 306B.

The indicator system 307 contained within the sensor probe 200 respondsto the excitation light by emitting light (as described in detailherein). In certain embodiments (as illustrated in FIG. 2A), theemission light signals generated by the indicator system 307 as well asthe excitation light signals are transmitted back out of the sensorprobe 200 into the fiber optic outlet lines 309A and 309B. In someembodiments, each fiber optic outlet line 309A and 309B substantiallycarries light corresponding to one type of fluorescent emission. Forexample, outlet line 309A carries light away from the sensor probe 200substantially consisting of a first type of fluorescent emission, andoutlet line 309B carries light away from the sensor probe 200substantially consisting of a second type of fluorescent emission. Inmeasuring devices configured with a mirror 308 beyond the indicatorsystem 307 at the far end of the sensor probe 200 (such as shown in FIG.2A), a portion of the light transmitted back out of the sensor probe 200into the fiber optic outlet lines 309A and 309B is light that has beenreflected by the mirror 308. However, other embodiments may lack amirror.

In the measurement device schematically illustrated in FIG. 2A, thefiber optic outlet lines 309A and 309B are augmented by including twointerference filters 312A and 312B; and two detectors 313A and 313B. Incertain embodiments, the interference filter 312A is configured tosubstantially block the excitation light generated by light source 301A(and, in some embodiments, additionally block the excitation andemission/fluorescence wavelengths corresponding to light source 301B)and substantially pass the fluorescence emitted and generated by theindicator system in response to irradiation by light source 301A. As aresult, this fluorescence passes to detector 313A where it is detected.The detector 313A may be any device capable of measuring fluorescentintensity at an appropriate wavelength or over an appropriate range ofwavelengths, including, but not limited to, detectors consisting of oneor more photodiodes. In certain embodiments, the detector 313A producesa signal that is amplified by the amplifier 314A and converted into adigital signal by analog-to-digital converter 315A and transmitted to areceiving and processing unit 316. The receiving and processing unit 316may comprise a data processing device of any type known in the art, forexample, a microprocessor, an embedded processor, a multiprocessor, ageneral purpose computer, a special purpose processor, any computationaldevice, a digital signal processor, a microcontroller, a programmablegate array or any combination thereof.

The interference filter 312B, detector 313B, amplifier 314B, andanalog-to-digital converter 315B may function in a similar manner withrespect to fluorescence emitted and generated by the indicator system307 in response to irradiation by light source 301B. In someembodiments, the receiving and processing unit 316, after receivingdigital signals from the analog-to-digital converters 315A and 315B mayemploy various calculation schemes disclosed herein to estimate ananalyte concentration, and in some embodiments, the glucoseconcentration of a sample. In some embodiments, the receiving andprocessing unit 316 may employ a temperature correction and/or pHcorrection method or algorithm such as those described in detail below.In addition, in some embodiments, the receiving and processing unit 316may transmit data and/or results to a storage unit which may store thedata and/or results (e.g. on an optical or magnetic disc or otherdigital medium). In some embodiments, the receiving and processing unit316 may transmit data and/or results to a display unit which may displaythe data and/or results (e.g. on a print-out or display screen).

Another embodiment of an measurement device is schematically illustratedin FIG. 2B. Like the device schematically illustrated in FIG. 2A, thedevice depicted in FIG. 2B is a two light source measurement device.However, the device depicted in FIG. 2B differs from that depicted inFIG. 2A in that it utilizes a spectrophotometer 310 instead of themultiple detectors 312A and 312B shown in FIG. 2A. In some embodiments,the spectrophotometer may be a ultraviolet/visible microspectrometersuch as those manufactured by Boehringer Ingelheim or Ocean Optic Inc.However, in principle, any spectrophotometer which measures opticalintensity over the appropriate wavelength range(s) may be used.

As schematically illustrated in FIG. 2B, the spectrophotometer 310receives light from the indicator system 307 via a single fiber opticoutlet line 309. In some embodiments, a spectrophotometer 310 such asthat depicted in FIG. 2B is capable of measuring optical intensity overa broader range of wavelengths than the detectors 312A and 312B.Accordingly, in some embodiments, one spectrophotometer 310 fed by asingle optical fiber 309 may provide the detection functionality ofmultiple detectors and in some embodiments much more flexibility.However, in some embodiments there are other device design tradeoffssuch as, for example, potential cost, complexity, size, and powerrequirements.

Also absent from the measurement device depicted in FIG. 2B are thefilters 312A and 312B; the amplifiers 314A and 314B; and theanalog-to-digital converters 315A and 315B exhibited by the deviceschematically illustrated in FIG. 2A. Similar functionality is provided,in some embodiments, by the spectrophotometer 310 itself. Thespectrophotometer 310 transmits data and/or results to a receiving andprocessing unit 316 as was described in reference to FIG. 2A. Thereceiving and processing units 316 of FIGS. 2A and 2B may functionsimilarly, as described above, depending on the embodiment.

Yet another embodiment of an analyte measuring device is schematicallyillustrated in FIG. 2C. Like the devices schematically illustrated inFIGS. 2A, and 2B, the device depicted in FIG. 2C is a two light sourcemeasurement device. However, the device depicted in FIG. 2C utilizes asingle fiber optic outlet line 309 which transmits light to a singlecollimator lens 317 and then on to beam splitters 318. In someembodiments, the beam splitter 318 substantially reflects lightgenerated by a first type of fluorescent emission, and substantiallytransmits light generated by a second type of fluorescent emission. Thereflected light is transmitted to a detector 313A, which generates ananalogue signal indicative of the intensity of the reflected light. Thesignal is amplified by the amplifier 314A and transmitted to theanalog-to-digital converter 315A where it is digitized. The digitalsignal is then transmitted to the receiving and processing unit 316.Light transmitted by the beam splitter 318 is detected by the detector313B, amplified by the amplifier 314B, digitized by theanalog-to-digital converter 315B, and transmitted to the receiving andprocessing unit 316 in parallel fashion to the light reflected by thebeam splitter 318. As described above, the receiving and processing unit316 may be a data processing device of any type known in the art, forexample, a microprocessor, an embedded processor, a multiprocessor, ageneral purpose computer, a special purpose processor, any computationaldevice, a digital signal processor, a microcontroller, a programmablegate array or any combination thereof.

The beam splitter 318 may be an interference filter designed to work ata substantially forty-five degree angle, as shown in FIG. 2C. In certainembodiments, the beam splitter 318 comprises a glass surface with acoating that reflects light having a certain wavelength and transmitsall other light. The beam splitter 318 can be positioned at asubstantially forty-five degree angle relative the direction of thelight traveling from the collimator lens 317. As described above, insome embodiments, the beam splitter 318 is configured in such a way thatlight generated by different types of fluorescent emission are detectedseparately by a dedicated detector 313A and 313B.

Notably absent from the embodiment schematically depicted in FIG. 2Cversus that depicted in FIG. 2B are the filters 312A and 312B. Incertain embodiments employing a beam splitter 318 renders additionalfiltering by the dedicated filters 312A and 312B unnecessary. Multiplefiber optic outlets lines may also be superfluous when a beam splitteris employed as is apparent from comparing the embodiments schematicallyillustrated in FIG. 2A (utilizing fiber optic outlet lines 309A and309B) and FIG. 2C (utilizing a single line 309). However, there aredesign trade-offs between the embodiments schematically illustrated inall three FIGS. 2A, 2B, and 2C as appreciated by one skilled in the art.Moreover, the embodiments illustrated in FIGS. 2A, 2B, and 2C are merelyillustrative of the types of device configurations which are possible.These example embodiments are not meant to be exhaustive and theparticular design chosen is not necessarily critical to the working ofthe various measurement devices disclosed herein.

Temperature Sensing Elements

In addition to an analyte sensing element, a pH sensing element, or acombination analyte and pH sensing element, the measurement device maycontain a temperature sensing element, such as, for example, athermistor or a thermocouple, located within the sensor probe 200. Insome embodiments, the temperature sensing element is located at or nearthe analyte sensing chemistry (i.e. the indicator system) such that thetemperature being measured is characteristic of the temperature of theanalyte solution where the concentration is being measured. In someembodiments, the temperature sensing element may be co-located with theindicator system within a distal tip of the sensor probe. A suitabletemperature sensing element is preferably small enough such that thesensor probe 200 does not have to be increased in size substantially toaccommodate it.

The temperature sensing element is particularly important when theanalyte sensing chemistry, such as a fluorophore system, is affected bytemperature change. As described above and in greater detail below, insome embodiments, the fluorescence intensity emitted by the fluorophoresystem is dependent on the temperature of the fluorophore system. Bymeasuring the temperature of the fluorophore system, temperature inducedvariations in fluorophore fluorescence intensity can be accounted for,allowing for more accurate determination of analyte concentration, asmore fully described below. For example, a fluorophore based glucosesensing chemistry may generate signals indicative of glucoseconcentration which are effected by the temperature at which the sensingis performed, and knowledge of the effect of temperature on thesesignals may be used to generate estimates of glucose concentration whichare corrected for temperature.

Sensor Probe

FIG. 3 illustrates in greater detail a sensor probe 200 in accordancewith an embodiment of the present invention. The sensor probe 200comprises an optical fiber 10 with a distal end 12 disposed in a porousmembrane sheath 14. The optical fiber 10 has cavities, such as holes 6A,in the fiber optic wall that can be formed by, for example, mechanicalmeans such as drilling or cutting. The holes 6A in the optical fiber 10can be filled with a suitable compound, such as a polymer. In someembodiments, the polymer is a hydrogel 8. In other embodiments of thesensor probe 200 as shown in FIG. 4, the optical fiber 10 does not haveholes 6A, and instead, the hydrogel 8 is disposed in a space distal tothe distal end 12 of the optical fiber 10 and proximal to the mirror 23.In some embodiments, the sensor probe 200 is configured to generate asignal indicative of glucose concentration. In some embodiments, thesensor probe 200 is configured for intravascular deployment.

In some embodiments, the porous membrane sheath 14 can be made from apolymeric material such as polyethylene, polycarbonate, polysulfone orpolypropylene. Other materials can also be used to make the porousmembrane sheath 14 such as zeolites, ceramics, metals, or combinationsof these materials. In some embodiments, the porous membrane sheath 14may be nanoporous. In other embodiments, the porous membrane sheath 14may be microporous. In still other embodiments, the porous membranesheath 14 may be mesoporous.

In some embodiments as shown in FIG. 4, the porous membrane sheath 14 isattached to the optical fiber 10 by a connector 16. For example, theconnector 16 can be an elastic collar that holds the porous membranesheath 14 in place by exerting a compressive force on the optical fiber10, as shown in FIG. 4. In other embodiments, the connector 16 is anadhesive or a thermal weld.

In some embodiments, such as that shown in FIG. 3, a mirror 23 and atemperature sensing element such as a thermistor 25 may be placed withinthe porous membrane sheath 14 distal the distal end 12 of the opticalfiber 10. Thermistor leads 27 can be made to run in a space between theoptical fiber 10 and porous membrane sheath 14. Although a thermistor 25is shown, other devices such as a thermocouple, pressure transducer, anoxygen sensor, a carbon dioxide sensor or a pH sensor for example can beused instead.

In some embodiments as shown in FIG. 4, the distal end 18 of the porousmembrane sheath 14 is open and can be sealed with, for example, anadhesive 20. In some embodiments, the adhesive 20 can comprise apolymerizable material that can fill the distal end 18 and then bepolymerized into a plug. Alternatively, in other embodiments the distalend 18 can be thermally welded by melting a portion of the polymericmaterial on the distal end 18, closing the opening and allowing themelted polymeric material to resolidify. In other embodiments as shownin FIG. 3, a polymeric plug 21 can be inserted into the distal end 18and thermally heated to weld the plug to the porous membrane sheath 14.Thermoplastic polymeric materials such as polyethylene, polypropylene,polycarbonate and polysulfone are particularly suited for thermalwelding. In other embodiments, the distal end 18 of the porous membranesheath 14 can be sealed against the optical fiber 10.

After the porous membrane sheath 14 is attached to the optical fiber 10and the distal end 18 of the porous membrane sheath 14 is sealed, thesensor probe 200 can be vacuum filled with a first solution comprising amonomer, a crosslinker and a first initiator. Vacuum filling of apolymerizable solution through a porous membrane and into a cavity in asensor is described in detail in U.S. Pat. No. 5,618,587 to Markle etal.; incorporated herein in its entirety by reference thereto. The firstsolution is allowed to fill the cavity 6 within the optical fiber 10.

In some embodiments, the first solution is aqueous and the monomer, thecrosslinker and the first initiator are soluble in water. For example,in some embodiments, the monomer is acrylamide, the crosslinker isbisacrylamide and the first initiator is ammonium persulfate. In otherembodiments, the monomer is dimethylacrylamide orN-hydroxymethylacrylamide. By increasing the concentrations of themonomer and/or crosslinker, the porosity of the resulting gel can bedecreased. Conversely, by decreasing the concentrations of the monomerand/or crosslinker, the porosity of the resulting gel can be increased.Other types of monomers and crosslinkers are also contemplated. In otherembodiments, the first solution further comprises an analyte indicatorsystem comprising a fluorophore and an analyte binding moiety thatfunctions to quench the fluorescent emission of the fluorophore by anamount related to the concentration of the analyte. In some embodiments,the fluorophore and analyte binding moiety are immobilized duringpolymerization, such that the fluorophore and analyte binding moiety areoperably coupled. In other embodiments, the fluorophore and analytebinding moiety are covalently linked. The indicator system chemistry mayalso be covalently linked to the polymeric matrix.

In some embodiments, after the sensor probe 200 is filled with the firstsolution, the optical fiber 10 and the first solution filled porousmembrane sheath 14 and cavity 6 are transferred to and immersed into asecond solution comprising a second initiator. In some embodiments, thesecond solution is aqueous and the second initiator istetramethylethylenediamine (TEMED). In some embodiments, the secondsolution further comprises the same fluorescent dye and/or quencherfound in the first solution and in substantially the sameconcentrations. By having the fluorescent dye and quencher in both thefirst solution and the second solution, diffusion of fluorescent dye andquencher out of the first solution and into the second solution can bereduced. In some embodiments where a second solution is used, the secondsolution further comprises monomer in substantially the sameconcentration as in the first solution. This reduces diffusion ofmonomer out of the first solution by reducing the monomer gradientbetween the first solution and the second solution.

In some embodiments, at or approximately at the interface between thefirst and second solutions, the first initiator and the second initiatorcan react together to generate a radical. In some embodiments, the firstinitiator and the second initiator react together in a redox reaction.In other embodiments, the radical can be generated by thermaldecomposition, photolytic initiation or initiation by ionizingradiation. In these other embodiments, the radical may be generatedanywhere in the first solution. Once the radical is generated, theradical can then initiate polymerization of the monomer and crosslinkerin the first solution.

When the radical is generated via a redox reaction as described herein,the polymerization proceeds generally from the interface between thefirst and second solutions to the interior of the porous membrane sheath14 and towards the cavity in the optical fiber 10. Rapid initiation ofpolymerization can help reduce the amount of first initiator that candiffuse from the first solution and into the second solution. Reducingthe amount of first initiator that diffuses out of the first solutionhelps reduce polymerization of monomer outside the porous membranesheath 14 which helps in forming a smooth external surface.Polymerization of the monomer and crosslinker results in a hydrogel 8that in some embodiments substantially immobilizes the indicator system,forming the sensor probe 200. Further variations on polymerizationmethodologies are disclosed in U.S. Patent Publ. No. 2008/0187655;incorporated herein in its entirety by reference thereto.

With reference to FIG. 5A, in certain embodiments, the sensor probe 200is a solid optical fiber with a series holes 6A drilled straight throughthe sides of the optical fiber. In certain embodiments, the holes 6A arefilled with the hydrogels 8. In certain embodiments, the series of holes6A that are drilled through the sensor probe 200 are evenly spacedhorizontally and evenly rotated around the sides of the sensor probe 200to form a spiral or helical configuration. In certain embodiments, theseries of holes 6A are drilled through the diameter of the sensor probe200. With reference to FIG. 5B, in certain embodiments, the sensor probe200 is a solid optical fiber with a series of holes 6A drilled throughthe sides of the fiber at an angle. In certain embodiments, the seriesof holes 6A drilled at an angle, which are filled with hydrogel 8, areevenly spaced horizontally and evenly rotated around the sides thesensor probe 200. With reference to FIG. 5C, in certain embodiments, theoptical fiber comprises a groove 6B along the length of the opticalfiber, wherein the groove 6B is filled with hydrogel 8. In certainembodiments, the depth of the groove 6B extends to the center of theoptical fiber. In certain embodiments, the groove 6B spirals around theoptical fiber. In certain embodiments, the groove 6B spirals around theoptical fiber to complete at least one rotation. In certain embodiments,the groove spirals 6B around the optical fiber to complete multiplerotations around the optical fiber.

With reference to FIG. 5D, in certain embodiments, the sensor probe 200is a solid optical fiber with triangular wedges 6C cut from the fiber.In certain embodiments, the triangular wedge areas 6C are filled withhydrogel 8. In certain embodiments, the triangular wedges cut-outs 6Care evenly spaced horizontally and around the sides of the sensor probe200. In certain embodiments, all light traveling in the sensor probe 200is transmitted through at least one hole 6A or groove 6B filled withhydrogel 8.

In certain embodiments, as illustrated in FIG. 6, the sensor probe 200comprises an optical fiber 10 having a distal end 12, an atraumatic tipportion 134 having a proximal end 136 and a distal end 138, a cavity 6between the distal end 12 of the optical fiber 10 and the proximal end136 of the atraumatic tip portion 134, and a rod 140 connecting thedistal end 12 of the optical fiber 10 to the proximal end 136 of theatraumatic tip portion 134. A hydrogel 8 containing the sensingchemistry, for example a fluorophore and quencher, fills the cavity 6.Also present within the cavity 6 is a temperature sensing element 25,such as thermocouple or thermistor. Covering the hydrogel filled cavity6 is a selectively permeable membrane 14 that allows passage of theanalyte being detected/sensed into and out of the hydrogel 8. It should,of course, be understood that the sensor probe 200 may be modified togenerate signals indicative of the analyte concentration of variousanalytes by selecting, for example, an appropriate sensing chemistry,and if necessary, choosing an appropriate selectively permeable membrane14.

The proximal portion of the sensor probe 200 comprises the proximalportion of the optical fiber 10. In some embodiments, the diameter, D1,of the distal portion of the sensor 2 is greater than the diameter, D2,of the proximal portion of the sensor 2. For example, the diameter D1 ofthe distal portion of the sensor probe 200 can be between about 0.0080inches and 0.020 inches, while the diameter D2 of the proximal portionof the sensor probe 200 can be between about 0.005 inches to 0.015inches. In some embodiments, the diameter D1 of the distal portion ofthe sensor probe 200 is about 0.012 inches, while the diameter D2 of theproximal portion of the sensor probe 200 is about 0.010 inches.

Indicator Systems

The indicator system includes the sensing moieties—including, in someembodiments, at least one type of fluorophore and at least one type ofbinding moiety. In some embodiments, when the sensing moieties contact asample containing the analyte of interest, a reversible,equilibrium-based, affinity-driven binding interaction between theanalyte and the at least one type of binding moiety is established. Thisbinding interaction alters the binding moieties' relationship with thefluorophores, such that when the fluorophores are excited by light fromthe at least one light source, their fluorescent emission varies withthe extent to which analyte has been bound by the binding moieties.Thus, emission from the one or more types of fluorophores is indicativeof the concentration of analyte in the sample.

Accordingly, in some embodiments the indicator system includes at leastone type of fluorophore which emits a fluorescence having an intensityin response to light from at least one light source. In certain suchembodiments, the intensity is detectable by at least one detector. Theindicator system further includes at least one type of binding moietycapable of binding the analyte. The at least one type of binding moietyis typically operably coupled to the at least one type of fluorophoresuch that when the sample contacts the at least one type of bindingmoiety the intensity (emitted in response to light from the at least onelight source, as described above) is indicative of the concentration ofthe analyte. For example, a glucose binding moiety such as 3,3′-oBBV(described in detail below) that is coupled to a fluorescent dye such asHPTS-triLysMA (described in detail below) will quench the emissionintensity of the fluorescent dye, wherein the extent of quenching isreduced upon glucose binding resulting in an increase in emissionintensity related to glucose concentration. In some embodiments, theindicator system may include an immobilizing medium configured toprevent some of the fluorophores and/or some of the binding moietiesfrom freely diffusing through the sample.

Fluorophores

“Fluorophore” refers to a substance that when illuminated by light at aparticular wavelength emits light at a longer wavelength; i.e. itfluoresces. Fluorophores include but are not limited to organic dyes,organometallic compounds, metal chelates, fluorescent conjugatedpolymers, quantum dots or nanoparticles and combinations of the above.Fluorophores may be discrete moieties or substituents attached to apolymer.

Fluorophores that may be used in preferred embodiments are capable ofbeing excited by light of wavelength at or greater than about 400 nm,with a Stokes shift large enough that the excitation and emissionwavelengths are separable by at least 10 nm. In some embodiments, theseparation between the excitation and emission wavelengths may be equalto or greater than about 30 nm. These fluorophores are preferablysusceptible to quenching by electron acceptor molecules, such asviologens, and are resistant to photo-bleaching. They are alsopreferably stable against photo-oxidation, hydrolysis andbiodegradation.

In some embodiments, the fluorophore may be a discrete compound.

In some embodiments, the fluorophore may be a pendant group or a chainunit in a water-soluble or water-dispersible polymer having molecularweight of about 10,000 Daltons or greater, forming a dye-polymer unit.In one embodiment, such dye-polymer unit may also be non-covalentlyassociated with a water-insoluble polymer matrix M¹ and is physicallyimmobilized within the polymer matrix M¹, wherein M¹ is permeable to orin contact with analyte solution. In another embodiment, the dye on thedye-polymer unit may be negatively charged, and the dye-polymer unit maybe immobilized as a complex with a cationic water-soluble polymer,wherein said complex is permeable to or in contact with the analytesolution. In one embodiment, the dye may be one of the polymericderivatives of hydroxypyrene trisulfonic acid. The polymeric dyes may bewater-soluble, water-swellable or dispersible in water. In someembodiments, the polymeric dyes may also be cross-linked. In preferredembodiments, the dye has a negative charge.

In other embodiments, the dye molecule may be covalently bonded to thewater-insoluble polymer matrix M¹, wherein said M¹ is permeable to or incontact with the analyte solution. The dye molecule bonded to M¹ mayform a structure M¹-L¹-Dye. L¹ is a hydrolytically stable covalentlinker that covalently connects the sensing moiety to the polymer ormatrix. Examples of L¹ include lower alkylene (e.g., C₁-C₈ alkylene),optionally terminated with or interrupted by one or more divalentconnecting groups selected from sulfonamide (—SO₂NH—), amide —(C═O)N—,ester —(C═O)—O—, ether —O—, sulfide —S—, sulfone phenylene —C₆H₄—,urethane —NH(C═O)—O—, urea —NH(C═O)NH—, thiourea —NH(C═S)—NH—, amide—(C═O)NH—, amine —NR—(where R is defined as alkyl having 1 to 6 carbonatoms) and the like, or a combination thereof. In one embodiment, thedye is bonded to a polymer matrix through the sulfonamide functionalgroups.

In some embodiments, useful dyes include pyranine derivatives (e.g.hydroxypyrene trisulfonamide derivatives and the like), which have thefollowing formula:

wherein R¹, R², R³ are each —NHR⁴, R⁴ is —CH₂CH₂(—OCH₂CH₂—)_(n)X¹;wherein X¹ is —OH, —OCH₃COOH, —CONH₂, —SO₃H, —NH₂, or OMe; and n isbetween about 70 and 10,000. In one embodiment, the dyes may be bondedto a polymer through the sulfonamide functional groups. In otherembodiments, the dye may be one of the polymeric derivatives ofhydroxypyrene trisulfonic acid. In some embodiments, the fluorescent dyemay be 8-hydroxypyrene-1,3,6-trisulfonate (HPTS). The counter-ions canbe H⁺, Na⁺, or any other cation. HPTS has a molecular weight of lessthan 500 Daltons, so it will not stay within the polymer matrix, but itcan be used with an anion exclusion membrane. The dyes may be used witha quencher comprising boronic acid, such as 3,3′-oBBV.

(the Na⁺ Salt of HPTS—“Pyranine”)

In some embodiments, dyes of the following generic structure may serveas suitable fluorophores:

wherein:

R² is

R³ is —(CH₂)_(n)-A⁻M⁺,

-   -   wherein n is 1-4,    -   wherein A⁻ is an anionic group selected from the group        consisting of SO₃ ⁻, HPO₃ ⁻, CO₂ ⁻ and

-   -   wherein M⁺ is a cationic group selected from the group        consisting of H⁺, an alkali metal ion, Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺,        Fr⁺, an onium ion and NR₄ ⁺, wherein R is selected from the        group consisting of alkyl, alkylaryl and aromatic groups);

R⁴ is

R⁵ is selected from the group consisting of and Y—(CH₂)_(n)—R⁶ and

-   -   wherein n is equal to 1-10, n′ is equal to 2-4 and Y is selected        from the group consisting of NH and O;        R⁶ is selected from the group consisting of NHR⁷, OR⁷ and CO₂H;        and        R⁷ is H or an ethylenically unsaturated group selected from the        group consisting of methacryloyl, acryloyl, styryl, acrylamide        and methacrylamido.

In some embodiments, dyes of the following generic structure may serveas suitable fluorophores:

where:R³ is —(CH₂)_(n)-A⁻M⁺,

-   -   wherein n is 1-4,    -   wherein A⁻ is an anionic group selected from the group        consisting of SO₃ ⁻, HPO₃ ⁻, CO₂ ⁻ and

-   -   wherein M⁺ is a cationic group selected from the group        consisting of H⁺, an alkali metal ion, Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺,        Fr⁺, an onium ion and NR₄ ⁺, wherein R is selected from the        group consisting of alkyl, alkylaryl and aromatic groups);

R⁴ is

R⁸ is selected from the group consisting of —(CH₂)_(n)—R⁹ and

-   -   wherein n is equal to 1-10, n′ is equal to 2-4;        R⁹ is selected from the group consisting of NHR¹⁰, OR¹⁰ and        CO₂H; and        R¹⁰ is H or an ethylenically unsaturated group selected from the        group consisting of methacryloyl, acryloyl, styryl, acrylamido        and methacrylamido.

In another embodiment, the fluorescent dye may be polymers of8-acetoxy-pyrene-1,3,6-N,N′,N″-tris-(methacrylpropylamidosulfonamide)(acetoxy-HPTS-MA):

It is noted that dyes such as acetoxy-HPTS-MA (above) having no anionicgroups, may not give very strong glucose response when operably coupledto a viologen quencher, particularly a viologen quencher having only asingle boronic acid moiety.

In another embodiment, the fluorescent dye may be8-hydroxy-pyrene-1,3,6-N,N′,N″-tris-(carboxypropylsulfonamide)(HPTS-CO₂):

In another embodiment, the fluorescent dye may be8-hydroxy-pyrene-1,3,6-N,N′,N″-tris-(methoxypolyethoxyethyl (˜125)sulfonamide) (HPTS-PEG):

It is noted that dyes such as HPTS-PEG (above) having no anionic groups,may not provide a very strong glucose response when operably coupled toa viologen quencher, particularly a viologen quencher having only asingle boronic acid moiety.

Representative dyes as discrete compounds are the tris adducts formed byreacting 8-acetoxypyrene-1,3,6-trisulfonylchloride (HPTS-Cl) with anamino acid, such as amino butyric acid. Hydroxypyrene trisulfonamidedyes bonded to a polymer and bearing one or more anionic groups are mostpreferred, such as copolymers of8-hydroxypyrene-1-N-(methacrylamidopropylsulfonamido)-N′,N″-3,6-bis(carboxypropylsulfonamide)HPTS-CO₂-MA with HEMA, PEGMA, and the like.

In another embodiment, the fluorescent dye may be HPTS-TriCys-MA:

This dye is also referred to as just HPTS-Cys-MA. The dye may be usedwith a quencher comprising boronic acid, such as 3,3′-oBBV.

Of course, in some embodiments, substitutions other than Cys-MA on theHPTS core are consistent with aspects of the present invention, as longas the substitutions are negatively charged and have a polymerizablegroup. Either L or D stereoisomers of cysteine may be used. In someembodiments, only one or two of the sulfonic acids may be substituted.Likewise, in variations to HPTS-CysMA shown above, other counter-ionsbesides NBu₄ ⁺ may be used, including positively charged metals, e.g.,Na⁺. In other variations, the sulfonic acid groups may be replaced withe.g., phosphoric, carboxylic, etc. functional groups.

Another suitable dye is HPTS-LysMA, which is pictured below as follows:

Other examples include soluble copolymers of 8-acetoxypyrene-1,3,6-N,N′,N″-tris(methacrylamidopropylsulfonamide) with HEMA, PEGMA, or otherhydrophilic comonomers. The phenolic substituent in the dye is protectedduring polymerization by a blocking group that can be removed byhydrolysis after completion of polymerization. Such suitable blockinggroups, as for example, acetoxy, trifluoroacetoxy, and the like, arewell known in the art.

Fluorescent dyes, including HPTS and its derivatives are known and manyhave been used in analyte detection. See e.g., U.S. Pat. Nos. 6,653,141,6,627,177, 5,512,246, 5,137,833, 6,800,451, 6,794,195, 6,804,544,6,002,954, 6,319,540, 6,766,183, 5,503,770, and 5,763,238; andco-pending U.S. patent application Ser. Nos. 11/296,898, 60/833,081, and11/671,880; each of which is incorporated herein in its entirety byreference thereto.

The SNARF and SNAFL dyes from Molecular Probes may also be usefulfluorophores in accordance with aspects of the present invention. Thestructures of SNARF-1 and SNAFL-1 are shown below.

Additionally, a set of isomeric water-soluble fluorescent probes basedon both the 6-aminoquinolinium and boronic acid moieties which showspectral shifts and intensity changes with pH, in awavelength-ratiometric and colorimetric manner may be useful inaccordance with some embodiments of the present invention (See e.g.,Badugu, R. et al. 2005 Talanta 65 (3):762-768; and Badugu, R. et al.2005 Bioorg. Med. Chem. 13 (1):113-119); incorporated herein in itsentirety by reference.

Another example of a fluorescence dye is tetrakis(4-sulfophenyl)porphine(TSPP)—shown below. TSPP may not work optimally in blood, where theporphyrin ring may react with certain metal ions, like ferric, andbecome non-fluorescent. However, it may work better when included in theindicator system of a bench top analyte measurement apparatus.

Other examples of fluorescent indicators that may be useful fordetermination of glucose concentration are described in US 2005/0233465and US 2005/0090014; each of which is incorporated herein by referencein its entirety.

Analyte Binding Moieties—Quenchers

In accordance with broad aspects of the present invention, the analytebinding moiety provides the at least dual functionality of being able tobind analyte and being able to modulate the apparent concentration ofthe fluorophore (e.g., detected as a change in emission signalintensity) in a manner related to the amount of analyte binding. Inpreferred embodiments, the analyte binding moiety is associated with aquencher. “Quencher” refers to a compound that reduces the emission of afluorophore when in its presence. Quencher (O) is selected from adiscrete compound, a reactive intermediate which is convertible to asecond discrete compound or to a polymerizable compound or Q is apendant group or chain unit in a polymer prepared from said reactiveintermediate or polymerizable compound, which polymer is water-solubleor dispersible or is an insoluble polymer, said polymer is optionallycrosslinked.

In one example, the binding moiety that provides glucose recognition inthe embodiments is an aromatic boronic acid. In some embodiments, thebinding moiety may be a quencher comprising a boronic acidfunctionalized to either a pyridinium cation (or salt) as disclosed inU.S. Patent Application Publication No. 2008/0305009 or a polyviologenas disclosed in US. Patent Application Publication No. 2009/0081803;each of which is hereby incorporated herein in its entirety by referencethereto. In some embodiments, the boronic acid is covalently bonded to aconjugated nitrogen-containing heterocyclic aromatic bis-onium structure(e.g., a viologen). “Viologen” refers generally to compounds having thebasic structure of a nitrogen containing conjugated N-substitutedheterocyclic aromatic bis-onium salt, such as 2,2′-, 3,3′- or 4,4′-N,N′bis-(benzyl) bipyridium dihalide (i.e., dichloride, bromide chloride),etc. Viologen also includes the substituted phenanthroline compounds. Insome embodiments, the boronic acid substituted quencher preferably has apKa of between about 4 and 9, and reacts reversibly with glucose inaqueous media at a pH from about 6.8 to 7.8 to form boronate esters. Theextent of reaction is related to glucose concentration in the medium.Formation of a boronate ester diminishes quenching of the fluorophore bythe viologen resulting in an increase in fluorescence dependent onglucose concentration. A useful bis-onium salt is compatible with theanalyte solution and capable of producing a detectable change in thefluorescent emission of the dye in the presence of the analyte to bedetected.

In some embodiments, a binding moiety may comprise an analyte bindingprotein operably coupled to a fluorophore, such as the glucose bindingproteins disclosed in U.S. Pat. Nos. 6,197,534, 6,227,627, 6,521,447,6,855,556, 7,064,103, 7,316,909, 7,326,538, 7,345,160, and 7,496,392,U.S. Patent Application Publication Nos. 2003/0232383, 2005/0059097,2005/0282225, 2009/0104714, 2008/0311675, 2008/0261255, 2007/0136825,2007/0207498, and 2009/0048430, and PCT International Publication Nos.WO 2009/021052, WO 2009/036070, WO 2009/021026, WO 2009/021039, WO2003/060464, and WO 2008/072338 which are hereby incorporated byreference herein in their entireties.

Bis-onium salts in the embodiments of this invention are prepared fromconjugated heterocyclic aromatic di-nitrogen compounds. The conjugatedheterocyclic aromatic di-nitrogen compounds are selected fromdipyridyls, dipyridyl ethylenes, dipyridyl phenylenes, phenanthrolines,and diazafluorenes, wherein the nitrogen atoms are in a differentaromatic ring and are able to form an onium salt. It is understood thatall isomers of said conjugated heterocyclic aromatic di-nitrogencompounds in which both nitrogens can be substituted are useful in thisinvention. In one embodiment, the quencher may be one of the bis-oniumsalts derived from 3,3′-dipyridyl, 4,4′-dipyridyl and4,7-phenanthroline.

In some embodiments, the viologen-boronic acid adduct may be a discretecompound having a molecular weight of about 400 Daltons or greater. Inother embodiments, it may also be a pendant group or a chain unit of awater-soluble or water-dispersible polymer with a molecular weightgreater than about 10,000 Daltons. In one embodiment, thequencher-polymer unit may be non-covalently associated with a polymermatrix and is physically immobilized therein. In yet another embodiment,the quencher-polymer unit may be immobilized as a complex with anegatively charge water-soluble polymer.

In other embodiments, the viologen-boronic acid moiety may be a pendantgroup or a chain unit in a crosslinked, hydrophilic polymer or hydrogelsufficiently permeable to the analyte (e.g., glucose) to allowequilibrium to be established.

In other embodiments, the quencher may be covalently bonded to a secondwater-insoluble polymer matrix M², which can be represented by thestructure M²-L²-Q. L² is a linker selected from the group consisting ofa lower alkylene (e.g., C₁-C₈ alkylene), sulfonamide, amide, quaternaryammonium, pyridinium, ester, ether, sulfide, sulfone, phenylene, urea,thiourea, urethane, amine, and a combination thereof. The quencher maybe linked to M² at one or two sites in some embodiments.

For the polymeric quencher precursors, multiple options are availablefor attaching the boronic acid moiety and a reactive group which may bea polymerizable group or a coupling group to two different nitrogens inthe heteroaromatic centrally located group. These are:

a) a reactive group on a first aromatic moiety is attached to onenitrogen and a second aromatic group containing at least one —B(OH)₂group is attached to the second nitrogen;

b) one or more boronic acid groups are attached to a first aromaticmoiety which is attached to one nitrogen and one boronic acid and areactive group are attached to a second aromatic group which secondaromatic group is attached to the second nitrogen;

c) one boronic acid group and a reactive group are attached to a firstaromatic moiety which first aromatic group is attached to one nitrogen,and a boronic acid group and a reactive group are attached to a secondaromatic moiety which is attached to the second nitrogen; and

d) one boronic acid is attached to each nitrogen and a reactive group isattached to the heteroaromatic ring.

Preferred embodiments comprise two boronic acid moieties and onepolymerizable group or coupling group wherein the aromatic group is abenzyl substituent bonded to the nitrogen and the boronic acid groupsare attached to the benzyl ring and may be in the ortho- meta or para-positions.

In some embodiments, the boronic acid substituted viologen as a discretecompound useful for in vitro sensing may be represented by one of thefollowing formulas:

where n=1-3, X is halogen, and Y¹ and Y² are independently selected fromphenyl boronic acid (o- m- or p-isomers) and naphthyl boronic acid. Inother embodiments, the quencher may comprise a boronic acid group as asubstituent on the heterocyclic ring of a viologen.

A specific example used with TSPP is m-BBV:

The quencher precursors suitable for making sensors may be selected fromthe following:

The quencher precursor 3,3′-oBBV may be used with HPTS-LysMA orHPTS-CysMA to make hydrogels in accordance with preferred aspects of theinvention.

Preferred quenchers are prepared from precursors comprising viologensderived from 3,3′-dipyridyl substituted on the nitrogens withbenzylboronic acid groups and at other positions on the dipyridyl ringswith a polymerizable group or a coupling group. Representative viologensinclude:

where L is L1 or L2 and is a linking group

Z is a reactive group; and

R′ is —B(OH)₂ in the ortho- meta- or para- positions on the benzyl ringand R″ is H—; or optionally R″ is a coupling group as is defined hereinor a substituent specifically used to modify the acidity of the boronicacid such as fluoro- or methoxy-

L is a divalent moiety that covalently connects the sensing moiety to areactive group that is used to bind the viologen to a polymer or matrix.Examples of L include those which are each independently selected from adirect bond or, a lower alkylene having 1 to 8 carbon atoms, optionallyterminated with or interrupted by one or more divalent connecting groupsselected from sulfonamide (—SO₂NH—), amide —(C═O)N—, ester —(C═O)—O—,ether —O—, sulfide —S—, sulfone (—SO₂—), phenylene —C₆H₄—, urethane—NH(C═O)—O—, urea —NH(C═O)NH—, thiourea —NH(C═S)—NH—, amide —(C═O)NH—,amine —NR— (where R is defined as alkyl having 1 to 6 carbon atoms) andthe like.

Z is either a polymerizable ethylenically unsaturated group selectedfrom but not limited to methacrylamido-, acrylamido-, methacryloyl-,acryloyl-, or styryl- or optionally Z is a reactive functional group,capable of forming a covalent bond with a polymer or matrix. Such groupsinclude but are not limited to —Br, —OH, —SH, —CO₂H, and —NH₂.

Boronic acid substituted polyviologens are another class of preferredquenchers. The term polyviologen includes: a discrete compound comprisedof two or more viologens covalently bonded together by a linking group,a polymer comprised of viologen repeat units in the chain, a polymerwith viologen groups pendant to the chain, a dendrimer comprised ofviologen units, preferably including viologen terminal groups, anoligomer comprised of viologen units, preferably including viologenendgroups, and combinations thereof. Polymers in which mono-viologengroups form a minor component are not included. The preferred quenchersare water soluble or dispersible polymers, or crosslinked, hydrophilicpolymers or hydrogels sufficiently permeable to glucose to function aspart of a sensor. Alternatively the polyviologen boronic acid may bedirectly bonded to an inert substrate.

A polyviologen quencher as a polymer comprised of viologen repeat unitshas the formula:

In another embodiment, the polyviologen boronic acid adducts are formedby covalently linking two or more viologen/boronic acid intermediates.The bridging group is typically a small divalent radical bonded to onenitrogen in each viologen, or to a carbon in the aromatic ring of eachviologen, or one bond may be to a ring carbon in one viologen and to anitrogen in the other. Two or more boronic acid groups are attached tothe polyviologen. Optionally, the polyviologen boronic acid adduct issubstituted with a polymerizable group or coupling group attacheddirectly to the viologen or to the bridging group. Preferably thepolyviologen moiety includes only one such group. Preferably, thebridging group is selected to enhance cooperative binding of the boronicacids to glucose.

The coupling moiety is a linking group as defined previously with theproviso that the linking group is optionally further substituted with aboronic acid, a polymerizable group, an additional coupling group, or isa segment in a polymer chain in which the viologen is a chain unit, apendant group, or any combination thereof.

Immobilizing Medium

The indicator system comprising some embodiments of the measurementdevices disclosed herein may include an immobilizing medium whosepresence may prevent some of the fluorophores and/or some of the bindingmoieties from freely diffusing through the sample. For instance, incertain such embodiments, the immobilizing medium may limit the mobilityof the sensing moieties (including one or more types of fluorophores andone or more types of binding moieties) such that they remain physicallyclose enough to one another to react (quenching). Where in vivo sensingis desired, the immobilizing medium is preferably insoluble in anaqueous environment (e.g., intravascular), permeable to the targetanalytes, and impermeable to the sensing moieties. Where in vitroanalyte measurement is desired, the immobilizing medium is preferablyinsoluble in the sample's solvent, permeable to the target analytes,and, again, impermeable to the sensing moieties. For example, a benchtop glucose meter for measuring glucose activity in aqueous solution maycomprise a water-insoluble organic polymer matrix that is permeable tothe target analytes and impermeable to the sensing moieties. Morespecifically, the HPTS-triLysMA dye and 3,3′-oBBV quencher may beeffectively immobilized within a DMAA (N,N-dimethylacrylamide) hydrogelmatrix (described in detail below). Such an embodiment may be useful fordevices configured for in vitro or in vivo sensing.

In some embodiments for use in vitro, and not involving a moving stream,the sensing moieties (including one or more types of fluorophores andone or more types of binding moieties) may be used as individual(discrete) components. For example, in some embodiments, theconcentration of analyte in a liquid sample may be measured by addingand mixing into the sample the one or more types of fluorophores andbinding moieties, exciting the one or more types of fluorophores withlight of the appropriate wavelengths, and detecting the intensity of thefluorescence emitted by the fluorophores. Analyte concentration may thenbe calculated from the measured intensity. Afterwards, the sample hasbeen contaminated with the one or more fluorophores and binding moietiesand may need to be discarded. Of course, if the sample is taken from alarger solution, the amount of discarded solution may be insignificant.

In other embodiments for use in vitro, polymeric matrices may be used totrap the sensing moieties so that the sensing moieties do notpermanently contaminate the sample, and so that the sensing moieties maybe reused to determine analyte concentration in another sample. Incertain such embodiments, the sensing moieties may be immobilizedallowing their use to measure analytes in a moving stream.

For in vivo applications, some embodiments of the indicator system maybe used in a moving stream of physiological fluid which contains one ormore analytes, such as polyhydroxyl organic compounds, whoseconcentration is to be measured. Other embodiments for in vivoapplications may be implanted in tissue such as muscle which containsthe aforementioned analytes. Thus, for in vivo applications, it is oftenpreferred that the sensing moieties do not escape from the sensorassembly. In some embodiments, this is accomplished by making thesensing moieties a part of an organic polymer sensing assembly. Solublefluorophores and binding moieties may be confined by a semi-permeablemembrane that allows passage of the analyte but blocks passage of thesensing moieties. This can be realized by using as sensing moietiessoluble molecules that are substantially larger than the analytemolecules (molecular weight of at least twice that of the analyte orgreater than 1000 preferably greater than 5000); and employing aselective semipermeable membrane such as a dialysis or anultrafiltration membrane with a specific molecular weight cutoff betweenthe two so that the sensing moieties are quantitatively retained. Note,however, that these embodiments will also find substantial utility in invitro applications where it is desirable to immobilize or constrain thesensing moieties so that they do not freely mix with the sample in a waythat they cannot be easily extracted. As stated above, suchconfigurations reduce contamination of the sample and to some extentallow the fluorophores and binding moieties to be reused for multiplesamples and analyte measurements.

Irrespective of whether analyte concentration is to determined in vivoor in vitro, if glucose is the analyte of interest, it is oftenadvantageous that the sensing moieties be immobilized. In someembodiments, the glucose sensing moieties may be immobilized in aninsoluble polymer matrix, which is freely permeable to glucose. Thepolymer matrix may include of organic, inorganic or combinations ofpolymers thereof. For in vivo measurements, it may be advantageous forthe matrix to be composed of biocompatible materials. Alternatively oradditionally, the matrix may be coated with a second biocompatiblepolymer that is permeable to the analytes of interest. For in vitromeasurements, the use of biocompatible materials may not be necessary oreven advantageous.

In some embodiments where the indicator system includes a polymermatrix, the function of the polymer matrix is to hold together andimmobilize the one or more fluorophores and one or more binding moietieswhile at the same time allowing contact and binding between the analyteand the one or more binding moieties. To achieve this effect, the matrixmust be insoluble in the solution containing the analyte, but also be inclose association with it through the establishment of a high surfacearea interface between matrix and analyte solution. For example, in someembodiments, an ultra-thin film or microporous support matrix may beused. In some embodiments, the matrix may be swellable in the analytesolution. For some embodiments used to measure analyte concentrations isaqueous solutions, a hydrogel matrix may be used. In some instances, thesensing polymers are bonded to a surface such as the surface of a lightconduit, or impregnated in a microporous membrane. Preferably, thematrix does not substantially interfere with transport of the analyte tothe binding sites so that equilibrium may be established between the twophases. Techniques for preparing ultra-thin films, microporous polymers,microporous sol-gels, and hydrogels are established in the art. Usefulmatrices are typically substantially permeable to the analyte beingexamined.

Hydrogel polymers are used in some embodiments. The term, hydrogel, asused herein refers to a polymer that swells substantially, but does notdissolve in water. Such hydrogels may be linear, branched, or networkpolymers, or polyelectrolyte complexes, with the proviso that theycontain no soluble or leachable fractions. Typically, hydrogel networksare prepared by a crosslinking step, which is performed on water-solublepolymers so that they swell but do not dissolve in aqueous media.Alternatively, the hydrogel polymers are prepared by copolymerizing amixture of hydrophilic and crosslinking monomers to obtain a waterswellable network polymer. Such polymers are formed either by additionor condensation polymerization, or by combination process. In theseembodiments, the one or more fluorophores and one or more bindingmoieties may be incorporated into the polymer by copolymerization usingmonomeric derivatives in combination with network-forming monomers.Alternatively, the one or more fluorophores and one or more bindingmoieties may be coupled to an already prepared matrix using a postpolymerization reaction. In either case, the one or more fluorophoresand one or more binding moieties can be viewed as units in the polymerchain, or as pendant groups attached to the chain.

The hydrogels useful in this invention are also monolithic polymers,such as a single network to which both sensing moieties are covalentlybonded, or as multi-component hydrogels. Multi-component hydrogelsinclude interpenetrating networks, polyelectrolyte complexes, andvarious other blends of two or more polymers to obtain a water swellablecomposite, which includes dispersions of a second polymer in a hydrogelmatrix and alternating microlayer assemblies.

Monolithic hydrogels are typically formed by free radicalcopolymerization of a mixture of hydrophilic monomers, including but notlimited to HEMA, PEGMA, methacrylic acid, hydroxyethyl acrylate, N-vinylpyrrolidone, acrylamide, N,N′-dimethyl acrylamide, and the like; ionicmonomers include methacryloylaminopropyl trimethylammonium chloride,diallyl dimethyl ammonium. chloride, vinyl benzyl trimethyl ammoniumchloride, sodium sulfopropyl methacrylate, and the like; crosslinkersinclude ethylene dimethacrylate, PEGDMA, trimethylolpropane triacrylate,and the like. The ratios of monomers are chosen to optimize networkproperties including permeability, swelling index, and gel strengthusing principles well established in the art. In one embodiment, thefluorophore is derived from an ethylenically unsaturated derivative of adye molecule, such as 8-acetoxypyrene-1,3,6-N,N′,N″-tris(methacrylamidopropylsulfonamide), the binding moiety is derivedfrom an ethylenically unsaturated viologen such as 4-N-(benzyl-3-boronicacid)-4′-N′-(benzyl-4-ethenyl)-dipyridinium dihalide (m-SBBV) and thematrix is made from HEMA and PEGDMA. The concentration of fluorophore ischosen to optimize emission intensity. The ratio of binding moiety tofluorophore is adjusted to provide sufficient binding to produce thedesired measurable signal.

In some embodiments, a monolithic hydrogel is formed by a condensationpolymerization. For example, acetoxy pyrene trisulfonyl chloride isreacted with an excess of PEG diamine to obtain a tris-(amino PEG)adduct dissolved in the unreacted diamine. A solution of excesstrimesoyl chloride and an acid acceptor is reacted with4-N-(benzyl-3-boronic acid)-4′-N′-(2 hydroxyethyl) bipyridinium dihalideto obtain an acid chloride functional ester of the viologen. The tworeactive mixtures are brought into contact with each other and allowedto react to form the hydrogel, e.g. by casting a thin film of onemixture and dipping it into the other.

In other embodiments, multi-component hydrogels wherein the fluorophoreis incorporated in one component and the binding moiety in another arepreferred for making the sensor of this invention. Further, thesesystems are optionally molecularly imprinted to enhance interactionbetween components and to provide selectivity for glucose over otherpolyhydroxy analytes. Preferably, the multicomponent system is aninterpenetrating polymer network (IPN) or a semi-interpenetratingpolymer network (semi-IPN).

The IPN polymers are typically made by sequential polymerization. First,a network comprising the binding moiety is formed. The network is thenswollen with a mixture of monomers including the fluorophore monomer anda second polymerization is carried out to obtain the IPN hydrogel.

The semi-IPN hydrogel is formed by dissolving a soluble polymercontaining a fluorophore in a mixture of monomers including a bindingmoiety monomer and polymerizing the mixture. In some embodiments, thesensing components are immobilized by an insoluble polymer matrix whichis freely permeable to polyhydroxyl compounds. Additional details onhydrogel systems have been disclosed in US Patent Publications Nos.US2004/0028612, and 2006/0083688 which are hereby incorporated byreference in their entireties.

The polymer matrix is comprised of organic, inorganic or combinations ofpolymers thereof. The matrix may be composed of biocompatible materials.Alternatively, the matrix is coated with a second biocompatible polymerthat is permeable to the analytes of interest. The function of thepolymer matrix is to hold together and immobilize the fluorophore andbinding moieties while at the same time allowing contact with theanalytes (e.g., polyhydroxyl compounds, H⁺ and OH⁺), and binding of thepolyhydroxyl compounds to the boronic acid. Therefore, the matrix isinsoluble in the medium and in close association with it by establishinga high surface area interface between matrix and analyte solution. Thematrix also does not interfere with transport of the analyte to thebinding sites so that equilibrium can be established between the twophases. In one embodiment, an ultra-thin film or microporous supportmatrix may be used. In another embodiment, the matrix that is swellablein the analyte solution (e.g. a hydrogel matrix) can be used for aqueoussystems. In some embodiments, the sensing polymers are bonded to asurface such as the surface of a light conduit, or impregnated in amicroporous membrane. Techniques for preparing ultra-thin films,microporous polymers, microporous sol-gels, and hydrogels have beenestablished in the prior art.

In one preferred embodiment, the boronic acid substituted viologen maybe covalently bonded to a fluorophore. The adduct may be a polymerizablecompound or a unit in a polymer. One such adduct for example may beprepared by first forming an unsymmetrical viologen from 4,4′-dipyridylby attaching a benzyl-3-boronic acid group to one nitrogen and anaminoethyl group to the other nitrogen atom. The viologen is condensedsequentially first with 8-acetoxy-pyrene-1,3,6-trisulfonyl chloride in a1:1 mole ratio followed by reaction with excess PEG diamine to obtain aprepolymer mixture. An acid acceptor is included in both steps toscavenge the byproduct acid. The prepolymer mixture is crosslinked byreaction with a polyisocyanate to obtain a hydrogel. The product istreated with base to remove the acetoxy blocking group. Incompletereaction products and unreacted starting materials are leached out ofthe hydrogel by exhaustive extraction with deionized water beforefurther use. The product is responsive to glucose when used as thesensing component as described herein.

Alternatively, such adducts are ethylenically unsaturated monomerderivatives. For example, dimethyl bis-bromomethyl benzene boronate isreacted with excess 4,4′-dipyridyl to form a half viologen adduct. Afterremoving the excess dipyridyl, the adduct is further reacted with anexcess of bromoethylamine hydrochloride to form the bis-viologen adduct.This adduct is coupled to a pyranine dye by reaction with the8-acetoxypyrene-tris sulfonyl chloride in a 1:1 mole ratio in thepresence of an acid acceptor followed by reaction with excessaminopropylmethacrylamide. Finally, any residual amino groups may bereacted with methacrylol chloride. After purification, the dye/viologenmonomer may be copolymerized with HEMA and PEGDMA to obtain a hydrogel.

For example U.S. Pat. No. 5,114,676 (incorporated by reference herein inits entirety) provides a fluorescent indicator which may be covalentlyattached to a particle or to a microcrystalline cellulose fiber. Asensor utilizing the indicator may comprise an optically transparentsubstrate, a thermoplastic layer and a hydrogel. Part of the particlewith the indicator attached thereto is imbedded in a thermoplastic layerthat is coated on the substrate and mechanically adhered using heat andpressure. The majority of the particle/indicator is imbedded within ahydrogel layer that is applied over the thermoplastic layer. Such asensor may be applied to the tip of an optical waveguide. Furthermore,with the recent availability of low cost UV LEDs, the dye can bemeasured with relatively inexpensive instrumentation that combines UVand blue LEDs and a photodiode module. In one embodiment of the presentinvention, the preferred sensing device comprises at least one lightsource, a detector, and a sensor comprising a fluorescent reporter dyesystem. In one embodiment, the fluorescent reporter dye system comprisesa fluorescent dye operably coupled to an analyte-binding quencher. Thedye may be covalently bound to the quencher or merely associated withthe quencher. The dye and quencher are preferably operably coupled,which means that in operation, the quencher is in close enough proximityto the dye to interact with and modulate its fluorescence. In oneembodiment, the dye and quencher may be constrained together within ananalyte-permeable hydrogel or other polymeric matrix. When excited bylight of appropriate wavelength, the fluorescent dye emits light (e.g.,fluoresces). The intensity of the light is dependent on the extent ofquenching which varies with the amount of analyte binding. In otherembodiments, the fluorescent dye and the quencher may be covalentlyattached to hydrogel or other polymeric matrix, instead of to oneanother.

Protective Housing

In some embodiments, the sensor probe 200 of the measurement deviceincludes a protective housing 500 which provides protection to theindicator system 307. In embodiments wherein the indicator system 307comprises an immobilizing medium, the protective housing 500 may furtherprotect the immobilizing medium. In certain such embodiments, theprotective housing 500 may be appropriately sized for in vitro bench toplaboratory use. In some embodiments, a protective housing 500 mayprovide a protective benefit to a sensor probe 200 that is designed forin vivo analyte measurement, and in some embodiments, more specifically,for a sensor probe 200 that is designed for intravascular analytemeasurement. In certain such embodiments, the protective housing 500 maybe constructed of physiologically compatible materials and may be sizedfor intravascular deployment. In embodiments wherein the sensor probe200 includes a temperature sensing element, the temperature sensingelement may be contained within the protective housing 500.

In some embodiments, such as the embodiments schematically depicted inFIGS. 7A and 7B, the protective housing 500 may be constructed of ahollow tube comprising a first material 501, and a second material 502coating the first material 501. In some embodiments, the second material502 may coat the first material 501 so as to form a continuoussubstantially impermeable outer wall of the hollow tube, except in aregion where a portion of the second material 502 has been selectivelyremoved in order to generate at least one opening in the outer wall,while retaining the first material 501 in that region. Three squarecutouts 503 in the outer wall of the tube arranged in a line can be seenin FIGS. 7A and 7B, but cutouts of other shapes, positioned in otherarrangements, are clearly feasible, depending on the embodiments. Insome embodiments, such as the embodiment schematically illustrated inFIG. 7A, the first material 501 may form a tubular mesh 501A. In someembodiments, such as the embodiment schematically illustrated in FIG.7B, the first material 501 may form a coil 501B. For each of theembodiments schematically illustrated in these figures, the firstmaterial 501 (whether in the form of a tubular mesh 501A or a coil 501B)is visible in the figures through the cutouts 503 in outer wall formedby the second material 502.

Examples of materials suitable for use as the coil or tubular mesh (i.e.the first material 501) include both metallic and non-metallicmaterials. Suitable metallic materials include stainless steel, gold,titanium and silver, and alloys such as nitinol, beryllium copper andMP-35-N alloys comprising cobalt, nickel, chromium, and molybdenum. Insome embodiments, stainless steel is preferred. Suitable non-metallicmaterials include synthetic polymers such as polyamides, polyesters,polyurethanes, polyolefins, nylon and fluoropolymers, for examplepolytetrafluoroethylene (PTFE). The first material 501 must, however, bechosen so that it is possible to selectively remove a region of thesecond material 502 which coats the first material, without the firstmaterial itself being removed in that region.

As mentioned above, the first material 501 can be in the form of a coil501B, see FIG. 7B, or a tubular mesh 501A, see FIG. 7A. When in the formof a coil 501B, the coil can be made from wires of the first material501 which preferably have either a round or flat cross-section. When inthe form of a tubular mesh 501A, the mesh structure advantageouslycomprises a number of filaments. The term “filament” is used to refer toany elongated strand irrespective of its cross-sectional configurationand structure. For example, the filaments may be round or flat incross-section. In one embodiment, the mesh can comprise a number ofhelically wound filaments, for example comprising a first group offilaments wound in an anticlockwise direction and a second group offilaments wound in an opposite, clockwise direction. The tubular mesh501A of FIG. 7A displays this configuration. Suitable mesh structuresare described in International publication No. WO/2004/054438 which isincorporated by reference herein in its entirety.

In some embodiments wherein the first material 501 is in the form of atubular mesh 501A, the density of filament crossovers may be varied inorder to control the properties of the resulting hollow tube. Forexample, a high density mesh may engender the hollow tube with greaterstrength while a low density mesh provide the hollow tube with greaterflexibility. Variation in the tightness of a coil can provide a similareffect.

Variation in mesh density and/or coil tightness may also vary theporosity of the mesh. This variation may be significant at the locationof the opening in the outer wall formed by the second material since theporosity of the mesh in this region will control the speed of diffusionof the analyte into the sensor. Porosity is also important forembodiments employing an immobilizing medium because, in certain suchembodiments, the mesh may need to be sufficiently dense (or the coilwinding sufficiently tight) to prevent seepage or leakage of theimmobilizing medium out of the sensor's protective housing. Thus, insome embodiments, coil tightness and/or mesh density must be chosensimultaneously to give the protective housing sufficient strength andflexibility to protect against impacts and abrasions, to allowsufficient diffusion of analytes into the protective housing, and tocontain the immobilizing medium so that it does not leak out of theprotective housing. Obviously, in embodiments lacking an immobilizingmedium, leakage of an immobilizing medium out of the protective housingneed not be considered.

Suitable materials for use as the second material generally includepolymeric materials. Examples include polyesters, polyolefins such aspolyethylene (PE), e.g. low density polyethylene (LDPE), fluoropolymerssuch as fluorinated ethylene propylene (FEP), polytetrafluoroethylene(PTFE) and perfluoroalkoxy polymer (PFA), polyvinylchloride (PVC),polyamides such as polyether block amide (PEBA), Pebax®, nylon andpolyurethane. Polyesters and polyolefins are preferred due to theirsuitability for extrusion over the coil or tubular mesh. The selectiveremoval of a portion of a polyester or polyolefin coating, e.g. by laserablation, is also straightforward. Polyolefins are particularlypreferred due to the ease of laser ablating these materials.

In order to form a continuous substantially impermeable tube prior toselective removal of a portion of the second material, the secondmaterial is first used to coat the coil or tubular mesh formed by thefirst material. The second material can either coat the outer surfacesof the first material, and in effect form a continuous substantiallyimpermeable tube around the coil or tubular mesh formed by the firstmaterial, or the second material can entirely encapsulate the firstmaterial, effectively forming a tube of the second material in which isembedded the coil or tubular mesh formed by the first material. In oneembodiment the second material can be applied to the first material bydip coating the coil or tubular mesh formed by the first material. Inthis embodiment, the second material may be a polyamide, which resultsin a very stiff tube. In another embodiment a tube of the secondmaterial can be provided, around which is formed the coil or tubularmesh of the first material. A further layer of the second material isthen applied over the first material, resulting in the first materialbeing sandwiched between two layers of the second material.

As mentioned above, it is necessary that it be possible to selectivelyremove a region of the second material while retaining the firstmaterial in that region. Accordingly, it is a requirement that thesecond material is different from the first material. In this context,“different from” means that the first and second materials have somedifference in physical properties such that it is possible toselectively remove a region of the second material. This difference maybe achieved by using an entirely different material, or by using thesame material but using different forms which have different physicalproperties. For example, in one embodiment the first material ismetallic and the second material is polymeric.

In addition to the first and second materials, it is possible to includefurther materials. For example, for some applications it may be usefulto include a radio opaque additive to enable the sensor incorporatingthe tube to be visible in vivo. For example, radio opaque additives suchas barium sulfate, bismuth subcarbonate, bismuth trioxide and tungstencan be added. Where present, these are preferably doped within thesecond material.

When constructing the protective housings described above, a portion ofthe second material is selectively removed in order to generate at leastone opening in a region of the outer wall of the protective housing,while retaining the first material in that region. As the first materialis present in the form of a coil or a tubular mesh, the first materialdoes not form a completely closed tube. Accordingly, when the secondmaterial is removed in said region, this effectively forms a break inthe continuous substantially impermeable wall of the tube. Where thesecond material simply coats the first material, it is necessary simplyto remove the coating provided by this second material in the regionwhere the opening is to be formed. Where the second material effectivelyencapsulates the first material, it is necessary to remove all of thesecond material which surrounds and encapsulates the first material inthe region of the protective housing where the opening is to be formed.

Preferably the indicator system 307 used to generate a signal indicativeof the concentration of the analyte of interest is located adjacent tothe opening 503 formed by selective removal of the second material. Thisallows the indicator system to measure analyte concentration near theregion of the opening in the wall of the tube. Presumably, theenvironment of the fluid in this region is substantially similar to theenvironment of the fluid further away from the sensor probe's protectivehousing 500, and therefore the analyte concentration determined in thisregion will likely accurately represent the analyte concentrationelsewhere in the fluid. For example, where the measurement device is anintravascular glucose sensor, the sensor probe 200 and protectivehousing 500 may be inserted into a blood vessel, for example, andglucose in the blood will preferably migrate through the opening in thesecond material, and into the hollow tube, where its concentration canbe determined by the indicator system in conjunction with the othercomponents of the measurement device. Where the measurement device is abench top glucose meter, the sensor probe 200 and protective housing 500may be dipped into a solution contained in a beaker or test tube, forexample, such that the opening in the second material is submerged. Thesolution will then pass through the opening in the second material, intothe hollow tube, and the glucose concentration of the solution may bedetermined by the indicator system in conjunction with the othercomponents of the glucose sensor.

In some embodiments, the size of the opening in the second material willgenerally be between 1 and 400 mm², for example between 25 and 225 mm².The size of the opening is preferably not too small or the solution intowhich the sensor is introduced will not be able to pass through theopening or will pass through in insufficient quantities for an accuratemeasurement to be made. Yet, the opening is preferably not to large orelse the immobilizing medium constraining the free diffusion of thesensing moieties may be able to seep out. In some embodiments, it isadvantageous that the opening be large enough to allow positioning ofthe indicator system such that it is adjacent to the opening.

In some embodiments, the second material forming the outer wall of theprotective housing 500 possesses only a single opening 503 allowingpassing of the analyte. In other embodiments, a plurality of openings503 may be generated in the outer wall of the protective housing500—i.e. more than one region of the second material has been removed.For example, the protective housings 500 of the sensor probes 200displayed in FIGS. 7A and 7B each possess three regions where the secondmaterial 502 has been removed, exposing the first material 501A, 501B,and creating three openings 503 for the passage of analytes. Generallyspeaking, configurations of multiple openings in the protective housingallow for indicator systems, or portions of indicator systems, to belocated at a number of points along the length of the protectivehousing, and for multiple measurements to be taken. Thus, it is possiblefor a number of indicator systems to be located within a singleprotective housing, each measuring the analyte in a portion of the fluidcontaining the analyte which enters the protective housing through adifferent opening in the housing. It is also possible that a singleindicator system may comprise multiple sub-systems, each of which isspatially separated within the protective housing, and each of whichmeasures the analyte in a portion of the fluid containing the analytewhich enters the protective housing through a different opening in thehousing.

Many embodiments of the protective housings 500 disclosed above may, inmany instances, provide a robust and durable enclosure for protectingthe sensitive components of the sensor probe 200. Such protectivehousings may protect an in vitro sensor probe from impacts and abrasionsoccurring during bench top laboratory use. Alternatively, suchprotective housings may provide the durability and maneuverabilitynecessary for intravascular use. However, it should be understood thatmany types of protective housings may be suitable for protecting theindicator systems disclosed herein, beyond those particular types ofprotective housings that have been disclosed above.

Methods of Estimating Analyte Concentration Incorporating TemperatureCorrection

Some embodiments of the measurement devices disclosed herein generate asignal indicative of analyte concentration which exhibits a temperaturedependence. For example, if two solutions of precisely the same analyteconcentration are measured at two different temperatures with the samemeasurement device, in some embodiments, the measurement device maygenerate differing signals indicative of the two analyte concentrations.Thus, the accuracy of determining a solution's true analyteconcentration based on such as signal may be improved by taking thetemperature of the solution into account.

It has been discovered that for some embodiments of the measurementdevices disclosed herein, and in particular, for glucose measurementdevices employing a quencher binding moiety operably coupled to afluorophore, the temperature dependence of the fluorescent signalapproximately follows a modified version of the classic Michaelis-Mentenequation from enzyme kinetics:

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{c_{T}*\left\lbrack {G_{i} - a_{T}} \right\rbrack}{a_{T} + b_{T} - G_{i}}} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

where

-   -   [Glu] is the estimated glucose concentration,    -   a_(T) is the first Michaelis-Menten parameter “a”, at a        temperature T,    -   b_(T) is the second Michaelis-Menten parameter “b”, at the same        temperature T,    -   c_(T) is the third Michaelis-Menten parameter “c”, at the same        temperature T, and    -   G_(i) is the fluorescent signal (i=1,2), either referenced or        unreferenced, where G₁ is the fluorescence emission at 550 nm        when the fluorophore is excited at 470 nm (which is the        absorption maximum of the fluorophore's base-form), and G₂ is        the fluorescence emission at 550 nm when the fluorophore is        excited at 420 nm (which is the absorption maximum of the        fluorophore's acid-form). Note, however, that other combinations        of excitation and emission wavelengths are also feasible for use        in Equation 1. In the Examples below, G₂ has been used, unless        indicated otherwise.

In itself, this is an interesting and surprising result. Variousembodiments of the measurement devices disclosed herein employ aquencher-fluorophore indicator system which measures analyteconcentration through the establishment of an equilibrium between theanalyte of interest, the binding moiety (e.g. quencher), and thefluorophore. In such a system, analyte concentration is not measured byenzymatic consumption or conversion of the analyte. In contrast, theclassic Michaelis-Menten equation specifically describes enzymekinetics, a non-equilibrium phenomena involving theconsumption/conversion of the enzyme's substrate by the enzyme.Therefore, it is not to be expected, indeed it is surprising, that anequation closely related to the classic Michaelis-Menten equation wouldeffectively describe the temperature dependence of these types ofquencher-fluorophore-based measurement devices and analyte sensingelements (or other measurement devices and analyte sensing elementsfunctioning through analogous equilibrium mechanisms). In any event,knowledge that these devices (and similar devices) exhibit a temperaturedependence which follows a modified Michaelis-Menten equation allows theuse of temperature correction methods and algorithms to improve theaccuracy of analyte concentration measurements. Such methods andalgorithms are disclosed herein, along with measurement devices whichimplement such methods and algorithms.

Accordingly, some embodiment methods of estimating an analyteconcentration include generating a signal indicative of analyteconcentration and a signal indicative of temperature. Since, in someembodiments, the signal indicative of analyte concentration exhibits thetemperature dependence just described, in some embodiments, the signalindicative of temperature may be used to adjust the signal indicative ofanalyte concentration to correct for temperature dependence. Thus, incertain such embodiments, the methods further include transforming thesignal indicative of the analyte concentration utilizing an equation ofthe form of a modified Michaelis-Menten equation, such as Equation 1above, depending on Michaelis-Menten parameters, such as the parameters“a”, “b”, and “c”, as described above with reference to Equation 1.

The temperature dependence of Equation 1 is exhibited through theMichaelis-Menten parameters a_(T), b_(T), and c_(T), as indicated by thesubscript “T” labeling these parameters. In some embodiments, thetemperature dependence may need to be determined through a temperaturecalibration. Thus, in certain embodiment methods, the values of one ormore of the Michaelis-Menten parameters may be set based on data whichincludes temperature calibration data and the signal indicative of atemperature.

For example, in some embodiment methods, the temperature calibrationdata may be generated by a temperature calibration method. Thetemperature calibration method may include selecting a first testanalyte sensing element, and creating and/or providing a set of at leastthree solutions of differing known analyte concentrations. In certainsuch embodiments, a first temperature is selected (T1), three solutionsof the set of at least three solutions are heated and/or cooled to atemperature substantially similar to the selected first temperature, anda first set of at least three signals is generated using the first testanalyte sensing element, each signal indicative of the concentration ofanalyte in a different one of the three solutions at the firsttemperature. Measurements are then made at a second temperature. Thus,in certain embodiments, a second temperature is selected (T2), threesolutions of the set of at least three solutions (each of the three maybe the same or different than a solution chosen for the firsttemperature) are heated and/or cooled to a temperature substantiallysimilar to the selected second temperature, and a second set of at leastthree signals is generated using the first test analyte sensing element,each signal indicative of the concentration of analyte in a differentone of the three solutions at the second temperature. Of course, morethan three solutions may be used in either of these steps. And more thantwo temperatures may also be employed. Generally, the more solutions ofdiffering concentration and the greater number of different temperaturesthat are employed, the greater the accuracy of the resulting calibrationdata.

Once the solutions having known analyte concentrations have beenmeasured, and the first and second sets of at least three signals havebeen generated, in some embodiments, the sets of signals are used todetermine (usually approximately) the relationship between one or moreof the Michaelis-Menten parameters and temperature. For example, in someembodiments, the temperature calibration method may further includecomputing values of each of a first, second, and third Michaelis-Mentenparameter at the first temperature (a_(T1), b_(T1), and c_(T1)) by analgorithm comprising fitting a modified Michaelis-Menten equation to afirst fit dataset comprising the first set of at least three signals. Incertain such embodiments, the temperature calibration method may furtherinclude computing values of each of a first, second, and thirdMichaelis-Menten parameter at the second temperature (a_(T2), b_(T2),and c_(T2)) by an algorithm comprising fitting a modifiedMichaelis-Menten equation to a second fit dataset comprising the secondset of at least three signals. Thus, in methods such as these, each ofthe three Michaelis-Menten parameters has been determined at least twotemperatures, providing data which may be used to create a model of thetemperature dependence of each of the three Michaelis-Menten parameters.

To model the temperature dependence of the Michaelis-Menten parameters,in some embodiments, the temperature calibration method may furtherinclude selecting an equation relating the first Michaelis-Mentenparameter (a_(T)) to temperature, the equation depending on a first setof temperature calibration parameters; and setting a value for eachcalibration parameter of the first set of calibration parameters basedon the value of the first Michaelis-Menten parameter at the firsttemperature (a_(T1)) and the value of the first Michaelis-Mentenparameter at the second temperature (a_(T2)). In some embodiments,similar steps are performed with respect to the second and thirdMichaelis-Menten parameters (b_(T) and c_(T)). Thus, for example, thetemperature calibration method may further include selecting an equationrelating the second Michaelis-Menten parameter (b_(T)) to temperature,the equation depending on a second set of temperature calibrationparameters; and setting a value for each calibration parameter of thesecond set of calibration parameters based on the value of the secondMichaelis-Menten parameter at the first temperature (b_(T1)) and thevalue of the second Michaelis-Menten parameter at the second temperature(b_(T2)). Similarly, in some embodiments, the temperature calibrationmethod may further include selecting an equation relating the thirdMichaelis-Menten parameter (c_(T)) to temperature, the equationdepending on a third set of temperature calibration parameters; andsetting a value for each calibration parameter of the third set ofcalibration parameters based on the value of the third Michaelis-Mentenparameter at the first temperature (c_(T1)) and the value of the thirdMichaelis-Menten parameter at the second temperature (c_(T2)).

Furthermore, in some embodiments, equations linear in temperature may beselected to relate the first, second, and third Michaelis-Mentenparameters to temperature. For instance, in some embodiments, the first,second, and third Michaelis-Menten parameters may be written as

a _(T) =a ₃₇*τ_(a) _(T) (T),

b _(T) =b ₃₇*τ_(b) _(T) (T), and

c _(T) =c ₃₇*τ_(c) _(T) (T)  (Equation 2)

where τ_(a) _(T) (T), τ_(b) _(T) (T), and τ_(c) _(T) (T) are“temperature correction factors” which approximately account for thetemperature dependence of a_(T), b_(T), and c_(T). When the relationshipbetween Michaelis-Menten parameter and temperature is written as such,each Michaelis-Menten parameter a_(T), b_(T), and c_(T), is determinedby multiplying the 37° C. Michaelis-Menten parameter a₃₇, b₃₇, and c₃₇,by its corresponding “temperature correction factor,” τ_(a) _(T) (T),τ_(b) _(T) (T), or τ_(c) _(T) (T) respectively. The 37° C.Michaelis-Menten parameters may be determined by fitting a modifiedMichaelis-Menten equation to a set of signals indicative of the analyteconcentration of a plurality of solutions of differing analyteconcentrations held at a temperature of 37° C., as described above withrespect to, for example, T1 and T2. Alternatively, the parameters a₃₇,b₃₇, and c₃₇ may be supplied by a factory calibration as described inprovisional U.S. patent application No. 61/184,747, “Algorithms forCalibrating an Analyte Sensor,” filed Jun. 5, 2009, which is herebyincorporated herein by reference in its entirety. As yet anotheralternative, a₃₇, b₃₇, and c₃₇ may be determine via a one-point in vivocalibration as also disclosed in the same application.

To determine the “temperature correction factors,” τ_(a) _(T) (T), τ_(b)_(T) (T), and τ_(c) _(T) (T), some embodiment methods may employ alinear approximation. For instance, the temperature correction factorsmay be written as

τ_(a) _(T) (T)=m _(a) _(T) *T+β _(a) _(T) ,

τ_(b) _(T) (T)=m _(b) _(T) *T+β _(b) _(T) , and

τ_(c) _(T) (T)=m _(c) _(T) *T+β _(c) _(T) ,  (Equation 3)

where the slopes, m_(a) _(T) , m_(b) _(T) , m_(c) _(T) , and intercepts,β_(a) _(T) , β_(b) _(T) , β_(c) _(T) , are collectively referred to as“temperature calibration coefficients” (“TempCos”).

In some embodiments, a temperature calibration method used to determinevalues of these TempCos may require that values of the Michaelis-Mentenparameters be determined at a second temperature (T2), different than37° C. Values of the parameters at the second temperature (a_(T2),b_(T2), and c_(T2)) may be determined by fitting a modifiedMichaelis-Menten equation to a set of signals indicative of the analyteconcentration of a plurality of solutions of differing analyteconcentrations held at the second temperature, as described above withrespect to, for example, T1 and T2. Once this is done, the temperaturecalibration coefficients m_(a) and b_(a) may be determined bynormalizing to a₃₇ both a_(T2) and a₃₇, yielding a_(T2)/a₃₇ and 1, andfitting a line to the normalized values versus the two temperatures, T2and 37° C. The fit may be determined using linear least squares or anyother method of fitting a line to a set of points. The temperaturecalibration coefficient m_(a) _(T) is set equal to the slope of theresulting line and the temperature calibration coefficient β_(a) _(T) isset equal to the intercept. The other temperature calibrationcoefficients, m_(b) _(T) and β_(b) _(T) , may be determined similarlyfrom values of b_(T2) and b₃₇, and m_(c) _(T) and β_(c) _(T) bedetermined from values of c_(T2) and c₃₇. Once the calibration iscomplete, a temperature corrected estimated glucose concentration([Glu]) may be computed from a fluorescent signal (G₁) measured attemperature (7), by using the TempCos (m_(a) _(T) , β_(a) _(T) , m_(b)_(T) , β_(b) _(T) , m_(c) _(T) and β_(c) _(T) ), the 37° C.Michaelis-Menten parameters 37° C. (a₃₇, b₃₇, and c₃₇), and thetemperature (T) in Equations 2 and 3 to compute a_(T), b_(T), and c_(T),and then plugging a_(T), b_(T), c_(T) and the measured fluorescentsignal (G_(i)) into Equation 1.

Thus, in some embodiments the first, second, and third sets oftemperature calibration parameters may include a slope and an interceptrelating temperature to the value of either the first, second, or thirdMichaelis-Menten parameter. However, equations of other forms may beselected to relate the first, second, or third Michaelis-Menten equationto temperature. In some embodiments, a quadratic or higher-orderpolynomial in temperature may be suitable and/or desirable.

When measurement devices are mass produced, it may not be feasible orpractical to individually calibrate each measurement device—i.e. useeach individual measurement device to generate individual calibrationdata. It may be more cost effective to select one or more test devicesfrom a batch of mass produced devices, generate calibration data usingthe one or more test devices, and provide that calibration data to eachindividual devices produced in the batch. In some embodiments,variability between measurement devices from the same production batchmay be, to a large extent, attributable to a particular part of themeasurement device. In particular, variability between devices may beattributable to the part of the measurement device which generates asignal indicative of analyte concentration—e.g. the analyte sensingelement—and/or the part of the measurement device that generates asignal indicative of temperature—e.g. the temperature sensing element.In these circumstances, as well as others, it may be advantageous to usea calibration method employing multiple test measurement devices, and/ormultiple test sensing elements, because calibration over multiple testdevices and/or sensing elements may yield more accurate calibration datathan calibration methods which only utilize a single test device and/orsensing element. Accordingly, in some embodiments, the calibrationmethod may further include selecting a second test analyte sensingelement; generating a third set of at least three signals using thesecond test analyte sensing element, each signal indicative of theconcentration of analyte in a different solution of known analyteconcentration at the first temperature (T1); and generating a fourth setof at least three signals using the second test analyte sensing element,each signal indicative of the concentration of analyte in a differentsolution of known analyte concentration at the second temperature (T2).Obviously, calibration methods may similarly employ more than two testdevices, or more particularly, for instance, more than two test analytesensing elements.

In a manner similar to methods utilizing a single test analyte sensingelement, after the solutions having known analyte concentrations havebeen measured and the first, second, third, and fourth sets of at leastthree signals have been generated, in some embodiments, the sets ofsignals are used to determine (usually approximately) the relationshipbetween one or more of the Michaelis-Menten parameters and temperature.For example, in some embodiments, the temperature calibration method mayfurther include (1) computing values of each of a first, second, andthird Michaelis-Menten parameter at the first temperature (a_(T1),b_(T1), and c_(T1)) by an algorithm comprising fitting a modifiedMichaelis-Menten equation to a first fit dataset comprising both thefirst set of at least three signals (which was generated with the firsttest analyte sensing element at T1) and the third set of at least threesignals (which was generated with the second test analyte sensingelement at T1); and (2) computing values of each of a first, second, andthird Michaelis-Menten parameter at the second temperature (a_(T2),b_(T2), and c_(T2)) by an algorithm comprising fitting a modifiedMichaelis-Menten equation to a second fit dataset comprising both thesecond set of at least three signals (which was generated with the firsttest analyte sensing element at T2) and fourth set of at least threesignals (which was generated with the second test analyte sensingelement at T2). Essentially, in these types of methods, the signalsgenerated with the second test analyte sensing element are used in acombined fit with the signals generated with the first test analytesensing element, which results in values for each of the first, second,and third Michaelis-Menten parameters which take both test analytesensing elements into account. Alternatively, in some embodiments, atemperature calibration method may take both test analyte sensingelements into account by fitting the signals generated from each testanalyte sensing element separately, and then averaging the results toobtain better estimates of the Michaelis-Menten parameters. Thus, insome embodiments, the step of computing values of each of a first,second, and third Michaelis-Menten parameter at the first temperature(a_(T1), b_(T1), and c_(T1)) by an algorithm may further include fittinga modified Michaelis-Menten equation to a third fit dataset comprisingthe third set of at least three signals, and averaging the results offitting the third fit dataset with the results of fitting the first fitdataset. In addition, the step of computing values of each of a first,second, and third Michaelis-Menten parameter at the second temperature(a_(T2), b_(T2), and c_(T2)) by an algorithm may further include fittinga modified Michaelis-Menten equation to a fourth fit dataset comprisingthe fourth set of at least three signals, and averaging the results offitting the fourth fit dataset with the results of fitting the secondfit dataset.

Other methods for estimating analyte concentration which incorporatetemperature correction features and temperature calibration steps arealso disclosed herein. In some embodiments, these methods are similar tothose already described above and incorporate similar features, however,additional features may also be disclosed and, in some embodiments, thedisclosed methods may be more general and described in more generalterms. Since there are many ways to feasibly implement the discoveriesdisclosed herein for use in estimating analyte concentration, thefollowing additional methods are described in order to illustrate thebreadth of implementations that are possible.

In some embodiments, for instance, a method of estimating an analyteconcentration from a signal indicative of the analyte concentration mayinclude transforming the signal using an equation of the form of amodified Michaelis-Menten equation wherein the values of one or moreMichaelis-Menten parameters have been adjusted for temperature.

In some embodiments, for instance, a method of estimating an analyteconcentration may include generating a signal indicative of the analyteconcentration and generating a signal indicative of a temperature, andtransforming the signal indicative of the analyte concentrationutilizing an equation of the form of a modified Michaelis-Mentenequation wherein at least one of the Michaelis-Menten parameters hasbeen substituted with a calibration equation functionally depending on aset of one or more temperature calibration parameters and the signalindicative of temperature. One could refer to such an equation as a“substituted” modified Michaelis-Menten equation since theMichaelis-Menten parameters have been explicitly substituted withequations depending on one or more other variables—temperature and thetemperature calibration parameters. However, although such a“substituted” equation exhibits a more complicated analytic form, itnevertheless will still express the basic functional relationships ofthe modified Michaelis-Menten equation.

In some embodiments, the step of transforming the signal indicative ofanalyte concentration may utilize a “substituted” modifiedMichaelis-Menten equation in which each of the first, second, and thirdMichaelis-Menten parameters have been substituted with first, second,and third calibration equations (respectively), each of the equationsdepending on sets of first, second, and third temperature calibrationparameters (respectively), and each also depending on the signalindicative of temperature. In certain embodiments, at least one of thefirst, second, and third calibration equations is a polynomial in thesignal indicative of temperature. In certain such embodiments, each ofthe first, second, and third calibration equations is a polynomial inthe signal indicative of temperature. In certain embodiments, at leastone of the first, second, and third calibration equations is a linearequation in the signal indicative of temperature. In certain suchembodiments, each of the first, second, and third calibration equationsis a linear equation in the signal indicative of temperature. Thus, forexample, if each Michaelis-Menten parameter of Equation 1 above isassumed to exhibit a linear relationship with temperature, then the“substituted” modified Michaelis-Menten equation might appear as

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{\begin{matrix}{\left( {{\chi_{c_{T},1} \cdot T} + \chi_{c_{T},0}} \right)*} \\\left\lfloor {G_{i} - \left( {{\chi_{a_{T},1} \cdot T} + \chi_{a_{T},0}} \right)} \right\rfloor\end{matrix}}{\begin{matrix}{\left( {{\chi_{a_{T},1} \cdot T} + \chi_{a_{T},0}} \right) +} \\{\left( {{\chi_{b_{T},1} \cdot T} + \chi_{b_{T},0}} \right) - G_{i}}\end{matrix}}} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

and, similarly, if each Michaelis-Menten parameter is assumed to exhibita quadratic relationship with temperature then the “substituted”modified Michaelis-Menten equation might appear as

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{\begin{matrix}{\left( {{\chi_{c_{T},2} \cdot T^{2}} + {\chi_{c_{T},1} \cdot T} + \chi_{c_{T},0}} \right)*} \\\left\lfloor {G_{i} - \left( {{\chi_{a_{T},2} \cdot T^{2}} + {\chi_{a_{T},1} \cdot T} + \chi_{a_{T},0}} \right)} \right\rfloor\end{matrix}}{\begin{matrix}{\left( {{\chi_{a_{T},2} \cdot T^{2}} + {\chi_{a_{T},1} \cdot T} + \chi_{a_{T},0}} \right) +} \\{\left( {{\chi_{b_{T},2} \cdot T^{2}} + {\chi_{b_{T},1} \cdot T} + \chi_{b_{T},0}} \right) - G_{i}}\end{matrix}}} & \left( {{Equation}\mspace{14mu} 5} \right)\end{matrix}$

where:

-   -   [Glu] is the estimated glucose concentration,    -   χ_(a) _(T) _(,2), χ_(a) _(T) _(,1), and χ_(a) _(T) _(,0) are        polynomial coefficients parameterizing a_(T)'s dependence on the        temperature T,    -   χ_(b) _(T) _(,2), χ_(b) _(T) _(,1), and χ_(b) _(T) _(,0) are        polynomial coefficients parameterizing b_(T)'s dependence on the        temperature T,    -   χ_(c) _(T) _(,2), χ_(c) _(T) _(,1), and χ_(c) _(T) _(,0) are        polynomial coefficients parameterizing c_(T)'s dependence on the        temperature T, and    -   G_(i) is the fluorescent signal (i=1,2), either referenced or        unreferenced, where G₁ is the fluorescence emission at 550 nm        when the fluorophore is excited at 470 nm (which is the        absorption maximum of the fluorophore's base-form), and G₂ is        the fluorescence emission at 550 nm when the fluorophore is        excited at 420 nm (which is the absorption maximum of the        fluorophore's acid-form). Note, however, that other combinations        of excitation and emission wavelengths are also feasible for use        in Equations 4 and 5.

As stated above, although, the “substituted” equations (Equations 4 and5) exhibit a more complicated analytic form, they nevertheless stillexhibit the basic functional relationships of the modifiedMichaelis-Menten equation (Equation 1). In other embodiments, thecalibration equations substituted into the modified Michaelis-Mentenequation may have a functional form other than a polynomial intemperature.

Thus, as described above, the calibration equations substituted into themodified Michaelis-Menten equation for the Michaelis-Menten parametersmay take a variety of functional forms and each may have varying numbersof temperature calibration parameters. Obviously, more complicatedequations may have a greater numbers of temperature calibrationparameters. In any event, depending on the embodiment, varioustemperature calibration methods may be used to determine the values ofthe first, second, and third sets of the one or more temperaturecalibration parameters. In certain such embodiments, each set oftemperature calibration parameters may be determined by fitting the“substituted” modified Michaelis-Menten equation to a plurality ofsignals, the plurality of signals indicative of analyte concentration ina plurality of solutions at a plurality of temperatures. Once values ofthe various temperature calibration parameters are determined,temperature corrected estimates of analyte concentrations may begenerated from signals indicative of analyte concentration andtemperature.

Example 1

This example concerns the temperature calibration of an equilibriumfluorescence glucose sensor—referred to herein as a GluCathsensor—employing an HPTS-Cys-MA dye operably coupled to a 3,3′-oBBVquencher. The dye and quencher are immobilized within a hydrogeldisposed along the distal region of an optical fiber, while the proximalend of the optical fiber is coupled to a light source. The temperaturedependence of this sensor's fluorescence response to glucose was assumedto be described by the modified Michaelis-Menten equation of Equation 1as described above. The Michaelis-Menten parameters were assumed to beara linear relationship to temperature as set forth in Equations 2 and 3above. Using this model of the glucose sensor's temperature dependence,the TempCos (m_(a) _(T) , β_(a) _(T) , m_(b) _(T) , β_(b) _(T) , m_(c)_(T) , and β_(c) _(T) ) were determined by the methodology describedabove in reference to Equations 2 and 3. Specifically, the effect oftemperature on the fluorescent signal was determined experimentally bymeasuring the signal at four temperatures (15° C., 25° C., 37° C., and45° C.) and four glucose concentrations (50 mg/dL, 100 mg/dL, 200 mg/dL,and 400 mg/dL). At each temperature and glucose level the stable signal,G₂, was recorded.

This data is displayed in FIGS. 8-10. FIG. 8 displays four plots offluorescent signal versus glucose concentration—one plot for each ofthese four temperatures. FIG. 9 displays the same data with eachconstant temperature plot normalized to the value of its fluorescentsignal at 50 mg/dL. FIG. 10 displays essentially the same raw data asFIG. 8, but instead displays four plots of fluorescent signal versustemperature—one plot for each of the four glucose concentrations.Apparent from FIG. 10, is that the fluorescent signal's temperaturedependence—at constant glucose concentration—is approximately linear.

Using the data plotted in FIG. 8, values of the Michaelis-Mentenparameters at 15° C., a₁₅, b₁₅, and c₁₅, were determined by fitting(using linear least squares) the modified Michaelis-Menten equation ofEquation 1 to the fluorescence data generated at 15° C. Similarly,values of a₂₅, b₂₅, and c₂₅ were determined by fitting Equation 1 to thefluorescence data generated at 25° C.; values of a₃₇, b₃₇, and c₃₇ weredetermined by fitting Equation 1 to the fluorescence data generated at37° C.; and finally, values of a₄₅, b₄₅, and c₄₅ were determined byfitting Equation 1 to the fluorescence data generated at 45° C.

The process was repeated over four additional glucose sensors of thesame design as the first to improve the accuracy of the calibration.Thus, fluorescent signals were generated with each of the fouradditional glucose sensors, at each of the same four temperatures (15°C., 25° C., 37° C., and 45° C.), and at each of the same four glucoseconcentrations (50 mg/dL, 100 mg/dL, 200 mg/dL, and 400 mg/dL). Thisdata corresponding to each of the four sensors was fit with Equation 1(as was done with the initial sensor) in order to generate values ofa₁₅, a₂₅, a₃₇, a₄₅, b₁₅, b₂₅, b₃₇, b₄₅, c₁₅, c₂₅, c₃₇, and c₄₅ for eachadditional glucose sensor. The data was averaged over all five sensorsfor each of these quantities to generate ā₁₅, ā₂₅, ā₃₇, ā₄₅, b ₁₅, b ₂₅,b ₃₇, b ₄₅, c ₁₅, c ₂₅, c ₃₇, and c ₄₅.

Determination of the temperature calibration parameters (TempCos)corresponding to Equations 2 and 3 was done using these averaged values.Thus, the temperature calibration parameters corresponding to the “a”Michaelis-Menten parameter—i.e. m_(a) _(T) , and β_(a) _(T) —weredetermined by normalizing each of the “a” parameters to ā₃₇ and fittinga line (again using linear least squares) to a plot of these values—i.e.ā₁₅/ā₃₇, ā₂₅/ā₃₇, 1, ā₄₅/ā₃₇ versus temperature—the slope and interceptbeing m_(a) _(T) and β_(a) _(T) , respectively. The same was done withthe temperature calibration parameters m_(b) _(T) and β_(b) _(T) ,corresponding to the “b” Michaelis-Menten parameter, and m_(c) _(T) andβ_(c) _(T) , corresponding to the “c” Michaelis-Menten parameter. Theresulting values for these TempCos are summarized in the Table 1, below.

TABLE 1 m_(a) _(T) = −0.009924 β_(a) _(T) = 1.367206 m_(b) _(T) =−0.006467 β_(b) _(T) = 1.239281 m_(c) _(T) = 0.007856 β_(c) _(T) =0.709328

An equation for computing a temperature corrected glucose concentrationfrom a fluorescent signal and these temperature calibration parametersmay be derived by substituting Equation 2 into Equation 1 which yields

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{c_{37}*{\tau_{c}(T)}*\left\lbrack {G_{i} - {a_{37}*{\tau_{a}(T)}}} \right\rbrack}{{a_{37}*{\tau_{a}(T)}} + {b_{37}*{\tau_{b}(T)}} - G_{i}}} & \left( {{Equation}\mspace{14mu} 6} \right)\end{matrix}$

and then, using Equation 3, further substituting for τ_(a)(T), τ_(b)(T),and τ_(c)(T) in Equation (6), which yields

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{c_{37}*\left( {{m_{c}*T} + b_{c}} \right)*\left\lbrack {G_{i} - {a_{37}*\left( {{m_{a}*T} + b_{a}} \right)}} \right\rbrack}{{a_{37}*\left( {{m_{a}*T} + b_{a}} \right)} + {b_{37}*\left( {{m_{b}*T} + b_{b}} \right)} - G_{i}}} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$

Example 2

This example also concerns the temperature calibration of an equilibriumfluorescence glucose GluCath sensor. Again, the GluCath sensor employsan HPTS-Cys-MA dye operably coupled to a 3,3′-oBBV quencher, with thedye and quencher immobilized within a hydrogel disposed along the distalregion of an optical fiber, while the proximal end of the optical fiberis coupled to a light source. The temperature dependence of thissensor's fluorescence response to glucose was assumed to be described bythe modified Michaelis-Menten equation of Equation 1 as described above.The Michaelis-Menten parameters were assumed to bear a linearrelationship to temperature as set forth in Equations 2 and 3 above.Using this model of the glucose sensor's temperature dependence, theTempCos, m_(a) _(T) , β_(a) _(T) , m_(b) _(T) , β_(b) _(T) , m_(c) _(T), and β_(c) _(T) , were determined by the methodology described above inreference to Equations 2 and 3. Specifically, the effect of temperatureon the fluorescent signal was determined experimentally by measuring thesignal at four temperatures (15° C., 25° C., 37° C., and 45° C.) andfour glucose concentrations (50 mg/dL, 100 mg/dL, 200 mg/dL, and 400mg/dL). At each temperature and glucose level the stable signal, G₂, wasrecorded. The raw data from this experiment is plotted in FIG. 11.

FIG. 12 plots glucose response—G₂ versus glucose concentration—for eachof the four temperatures. This figure illustrates that the fluorescentsignal G₂ is inversely related to temperature and also that there arelarge differences in the fluorescent signal G₂ at all glucose levelsover the range of temperatures likely to be encountered in the intensivecare unit—i.e. 15° C. to 45° C. At each fixed temperature, the modifiedMichaelis-Menten equation (equation 1) was fit to the fluorescent signalG₂ versus glucose concentration to determine best-fit values of theMichaelis-Menten parameters a_(T), b_(T), and c_(T) at each temperature.The four best-fit modified Michaelis-Menten equations are overlaid onthe data in FIG. 12. The quality of the fits is evident from the figure.

FIG. 13 plots each of a_(T), b_(T), and c_(T) versus temperature, thevalues of the Michaelis-Menten parameters corresponding to the best-fitsdisplayed in FIG. 12. The plots of each of a_(T), b_(T), and c_(T)versus temperature illustrate that, in some embodiments, best-fit valuesof the Michaelis-Menten parameters change approximately linearly withtemperature. The best-fit values of the Michaelis-Menten parameters ateach temperature were normalized to their values at 37° C. and thenormalized values were fit using linear regression to compute slopes andintercepts as shown in FIG. 14.

The slopes and intercepts displayed in FIG. 14 correspond to the“temperature calibration coefficients” m_(a) _(T) , m_(b) _(T) , m_(c)_(T) , β_(a) _(T) , β_(b) _(T) , and β_(c) _(T) , i.e. “TempCos,” asdescribed above. The particular values computed from the data in thisexample are listed in Table 2, below.

TABLE 2 m_(a) _(T) = −0.008785 β_(a) _(T) = 1.32509 m_(b) _(T) =−0.007444 β_(b) _(T) = 1.275413 m_(c) _(T) = 0.010681 β_(c) _(T) =0.604815

The TempCos can then be used to predict the temperature dependentMichaelis-Menten parameters a_(T), b_(T), and c_(T) by multiplying the37° C. Michaelis-Menten parameters a₃₇, b₃₇, and c₃₇, by a temperaturecorrection factor, τ_(a) _(T) , τ_(b) _(T) (T), or τ_(c) _(T) (T),respectively, as indicated by Equation 3. Again, the 37° C.Michaelis-Menten parameters a₃₇, b₃₇, and c₃₇ may be measured atcalibration, determined by a factory calibration, or potentiallysupplied by any other appropriate method.

In order to illustrate the accuracy of employing the above-describedtemperature correction methodology, these TempCos were used to performtemperature correction on an independent data set, as illustrated inFIG. 15. In the independent data set, the G₂ fluorescent signal versusplasma glucose concentration was measured at four reference plasmaglucose levels (50 mg/dL, 100 mg/dL, 200 mg/dL, and 400 mg/dL) and atfour temperatures (15° C., 25° C., 37° C., and 45° C.). The referencemeasurements of plasma glucose level are indicated as single points(small and medium sized circles) in FIG. 15. Temperature measurements asdetermined by thermocouple are also displayed.

The other curve displayed in FIG. 15 is the temperature corrected plasmaglucose concentration. To compute this curve, the four reference plasmaglucose levels at 37° C. (indicated by medium sized circles in FIG. 15)were fit to a modified Michaelis-Menten equation (Equation 1, aspreviously described) to generate values of the 37° C. Michaelis-Mentenparameters (a₃₇, b₃₇, and c₃₇). The temperature corrected plasma glucoseconcentration curve in FIG. 15 was then computed at each temperatureread by the thermocouple by inputting into Equations 2 and 3 these 37°C. Michaelis-Menten parameters (a₃₇, b₃₇, and c₃₇), the TempCos m_(a)_(T) , m_(b) _(T) , m_(c) _(T) , β_(a) _(T) , β_(b) _(T) , and β_(c)_(T) , as determined in the table above), and the correspondingtemperature read by the thermocouple. The temperature corrected plasmaglucose concentration curve matches closely the reference plasma glucoselevels (indicated by the small and medium sized circles) in FIG. 15. Infact, the mean absolute relative deviation (“MARD”) between the computedtemperature corrected plasma glucose concentrations and the referenceplasma glucose levels was only 2.46% (excluding the 37° C. referencevalues used for calibration). The MARD for the same data set withouttemperature correction was 170%.

Methods of Measuring pH

If a solution's measured analyte concentration is to be corrected for pHeffects, the pH of the solution must be measured or estimated in somemanner. In some embodiments a separate pH sensor may be used to measurepH. In other embodiments, the same indicator system which is used togenerate a signal indicative of analyte concentration may be used tomeasure pH. For instance, the ratio of two green signals generated bythe indicator system may be used to compute pH through the followingrelationship:

$\begin{matrix}{{pH} = {{m_{pH}*\frac{G_{1}}{G_{2}}} + \beta_{pH}}} & \left( {{Equation}\mspace{14mu} 8} \right)\end{matrix}$

where m_(pH) is the slope and β_(pH) is the intercept of pH versusG₁/G₂. The ratio, G₁/G₂, is calculated from G₁ which is the fluorescenceemission at 550 nm when the fluorophore is excited at 470 nm, and G₂which is the fluorescence emission at 550 nm when the fluorophore isexcited at 420 nm. The approximate linearity of the relationship betweenG₁/G₂ and pH is illustrated in FIG. 16 over a range of glucoseconcentrations (50 mg/dL, 100 mg/dL, 200 mg/dL, and 400 mg/dL) and pHlevels (6.8, 7.2, 7.4, and 7.8), although some greater deviation fromlinearity occurs between pH 7.4 and pH 7.8. Note, that G₁/G₂ isrepresented in FIG. 16 as Ibase/Iacid since, as indicated above, 470 nmis the absorption maximum of the fluorophore's base-form, and 420 nm isthe absorption maximum of the fluorophore's acid-form. Also, note thatthe values of G₁/G₂ plotted in FIG. 16 have been normalized to the 100mg/dL, pH 7.4 value of G₁/G₂. Thus, Equation 8 may be used to predict pHlevel from the G₁/G₂ ratio once the constants m_(pH) and β_(pH) havebeen determined. In some embodiments, each analyte measurement devicemay be individually calibrated to determine the constants m_(pH) andβ_(pH) appropriate for that individual device. In other embodiments, anentire batch of measurement devices may be calibrated by selectingseveral devices from the batch, determining values of m_(pH) and β_(pH)for each selected device, and averaging the values of m_(pH) and β_(pH)obtained for each selected devices to produce averaged values of m_(pH)and β_(pH) valid for the entire batch of measurement devices for usewith Equation 8. In still other embodiments, averaged values of m_(pH)and β_(pH) may be determined as just described, but a one-pointcalibration is performed to individually calibrate each sensor in thebatch while taking advantage of the averaged values of m_(pH) and β_(pH)obtained for the entire batch. For instance, in some embodiments, theone point calibration performed on each individual measuring device mayinvolve using the individual device to measure G₁ and G₂ for a standardsolution having a glucose concentration of 100 mg/dL at pH 7.4. Thesevalues may then be used in Equation 9

$\begin{matrix}{{pH} = {{m_{pH}*\frac{\frac{G_{1}}{G_{2}}}{\frac{G_{1,7.4}}{G_{2,7.4}}}} + \beta_{pH}}} & \left( {{Equation}\mspace{14mu} 9} \right)\end{matrix}$

where:

-   -   G₁ is the fluorescent emission, either referenced or        unreferenced, at 550 nm when the fluorophore is excited at 470        nm, which is the absorption maximum of the fluorophore's        base-form (although other combinations of excitation and        emission wavelengths are also feasible for use as the numerator        of the G₁/G₂ ratio in Equation 9),    -   G₂ is the fluorescence emission, either referenced or        unreferenced, at 550 nm when the fluorophore is excited at 420        nm, which is the absorption maximum of the fluorophore's        acid-form (although other combinations of excitation and        emission wavelengths are also feasible for use as the        denominator of the G₁/G₂ ratio in Equation 9),    -   G_(1,7.4) G₁ signal at pH 7.4 and 100 mg/dL glucose        concentration,    -   G_(2,7.4) G₂ signal at pH 7.4 and 100 mg/dL glucose        concentration,    -   m_(pH)=pH slope, and    -   β_(pH)=pH intercept.

Thus, once universal values of m_(pH) and β_(pH) are determined for thebatch of measurement devices, and G_(1,7.4) and G_(2,7.4) are determinedvia one-point calibration for the individual measurement device, ameasured ratio G₁/G₂ may be used in Equation 9 to compute the pH levelof the solution of analyte. It was also discovered that thedetermination of pH from G₁/G₂ is effected by the temperature of thesolution—see for instance, Example 3, below. Moreover, for purposes ofestimating pH from the measured ratio G₁/G₂, the temperature dependencemay be taken into account by allowing m_(pH) and β_(pH) to vary withtemperature. In particular, the temperature dependence of m_(pH) andβ_(pH) may be modeled using Equations 10 and 11:

$\begin{matrix}{m_{pH} = {\frac{h}{T} + i}} & \left( {{Equation}\mspace{14mu} 10} \right) \\{\beta_{pH} = {{j*\sqrt{T}} + k}} & \left( {{Equation}\mspace{14mu} 11} \right)\end{matrix}$

where h, i, j, and k are empirically determined constants—see, forinstance, Example 3, below. Substituting Equations 10 and 11 intoEquation 9 gives an expression for computing pH from the ratio G₁/G₂which accurately, albeit approximately, takes temperature into account.

$\begin{matrix}{{pH} = {{\left( {\frac{h}{T} + i} \right)*\frac{\left( \frac{G_{1}}{G_{2}} \right)}{\left( \frac{G_{1,7.4}}{G_{2,7.4}} \right)}} + {j*\sqrt{T}} + k}} & \left( {{Equation}\mspace{14mu} 12} \right)\end{matrix}$

Example 3

In order to accurately determine pH from the measured G₁/G₂ ratio usingEquation 12, so as to take temperature into account, testing wasconducted to empirically determine the constants, h, i, j, and k. In theexperiment displayed in FIGS. 17 and 18, G₁ and G₂ were measured with aGluCath sensor at four temperatures (15° C., 25° C., 37° C., and 45° C.)and four pH levels (6.8, 7.0, 7.4, 7.6), all at a glucose concentrationof 100 mg/dL. Note that FIGS. 17 and 18 demonstrate, among other things,that the G₁ and G₂ fluorescent signals are effected by temperaturechange, even when the pH level is held constant. FIG. 19 shows the ratioof the measured values of G₁ and G₂ from FIGS. 17 and 18 plotted versuspH at each of the four temperatures. A line was fit (using linearregression) to each series of G₁/G₂ values corresponding to the sametemperature. FIG. 19 illustrates that the intercepts of these lines, andto a lesser extent the slopes of these lines, vary with temperature. Tomodel this temperature dependence, the associated slopes and interceptsare plotted as functions of temperature in FIG. 20. Equation 10 was usedto model the temperature dependence of the slope m_(pH), and based onthe data displayed in FIG. 20 best fit values of the constants h, and iwere determined. Similarly, Equation 11 was used to model thetemperature dependence of the intercept β_(pH), and based on the datadisplayed in FIG. 20 best fit values of the constants j, and k weredetermined. The best fit values of h, i, j, and k to be used in Equation12 are listed in Table 3.

TABLE 3 h = −10.9415 j = −0.16908 i = 2.3264 k = 6.3983

An independent data set was generated to test the accuracy of usingEquation 12 to compute pH level from measured G₁/G₂ ratio, using thesevalues of h, i, j, and k. FIG. 21 displays both measured reference pHvalues (small and medium sized dots) and values of pH computed fromG₁/G₂ with Equation 12 (sequence of ‘x’ marks)—at two temperatures (30°C., and 40° C.) and two glucose levels (50 mg/dL and 100 mg/dL). Notethat the medium sized dot (corresponding to a glucose concentration of100 mg/dL and pH 7.4) served as the reference point for the one-pointcalibration as described above. The results are displayed in thefollowing table. As indicated in Table 4, the average pH offset for thisdata set was +0.008.

TABLE 4 Glucose Temp Reference pH Calculated (mg/dL) (° C.) pH fromG₁/G₂ Difference 100 40 7.400 7.405 0.005 100 30 7.400 7.394 −0.006 10030 7.035 7.060 0.025 100 40 7.035 7.056 0.021 50 40 7.035 7.047 0.012 5030 7.035 7.043 0.008 50 30 7.400 7.395 −0.005 50 40 7.400 7.407 0.007Avg 0.008

Methods of Estimating Analyte Concentration Incorporating pH Correction

Some embodiments of the measurement devices disclosed herein generate asignal indicative of analyte concentration which exhibits a pHdependence. For example, if two solutions of precisely the same analyteconcentration are measured at two different pH levels with the samemeasurement device, in some embodiments, the measurement device maygenerate differing signals indicative of the two analyte concentrations.Thus, the accuracy of determining a solution's true analyteconcentration based on such as signal may be improved by taking the pHof the solution into account.

It has been discovered that for some embodiments of the measurementdevices disclosed herein, and in particular, for glucose measurementdevices employing a quencher binding moiety operably coupled to afluorophore, the pH dependence of the fluorescent signal approximatelyfollows a modified version of the classic Michaelis-Menten equation fromenzyme kinetics:

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{c_{pH}*\left\lfloor {G_{i} - a_{pH}} \right\rfloor}{a_{pH} + b_{pH} - G_{i}}} & \left( {{Equation}\mspace{14mu} 13} \right)\end{matrix}$

where:

-   -   [Glu] is the estimated glucose concentration,    -   a_(pH) is the first Michaelis-Menten parameter “a”, at a        particular pH,    -   b_(pH) is the second Michaelis-Menten parameter “b”, at the same        particular pH,    -   c_(pH) is the third Michaelis-Menten parameter “c”, at the same        particular pH, and    -   G_(i) is the fluorescent signal (i=1,2), either referenced or        unreferenced, where G₁ is the fluorescence emission at 550 nm        when the fluorophore is excited at 470 nm (which is the        absorption maximum of the fluorophore's base-form), and G₂ is        the fluorescence emission at 550 nm when the fluorophore is        excited at 420 nm (which is the absorption maximum of the        fluorophore's acid-form). Note, however, that other combinations        of excitation and emission wavelengths are also feasible for use        in Equation 13. In the Examples below, G₂ has been used, unless        indicated otherwise.

As with temperature dependence, the fact that pH dependence may bedescribed by a modified Michaelis-Menten equation is an interesting andsurprising result. Various embodiments of the measurement devicesdisclosed herein employ a quencher-fluorophore indicator system whichmeasures analyte concentration through the establishment of anequilibrium between the analyte of interest, the binding moiety (e.g.quencher), and the fluorophore. In such a system, analyte concentrationis not measured by enzymatic consumption or conversion of the analyte.In contrast, the classic Michaelis-Menten equation specificallydescribes enzyme kinetics, a non-equilibrium phenomena involving theconsumption/conversion of the enzyme's substrate by the enzyme.Therefore, it is not to be expected that an equation closely related tothe classic Michaelis-Menten equation would effectively describe the pHdependence of these types of quencher-fluorophore-based measurementdevices and analyte sensing elements (or other measurement devices andanalyte sensing elements functioning through analogous equilibriummechanisms). In any event, knowledge that these devices (and similardevices) exhibit a pH dependence which follows a modifiedMichaelis-Menten equation allows the use of pH correction methods andalgorithms to improve the accuracy of analyte concentrationmeasurements. Such methods and algorithms are disclosed herein, alongwith measurement devices which implement such methods and algorithms.

Accordingly, some embodiment methods of estimating an analyteconcentration include generating a signal indicative of analyteconcentration and a signal indicative of pH. In some embodiments, thesignal indicative of the analyte concentration and the signal indicativeof the pH are both generated from a set of at least two signals each ofwhich is indicative of both the pH and the analyte concentration. Forinstance, these could be the G₁ and G₂ fluorescent signals describedabove, both of which are indicative of both analyte concentration andpH. In some embodiments, the G₂ fluorescent signal itself may be treatedas the signal indicative of analyte concentration, while G₁ and G₂ areused as signals indicative of pH, for example, in the pH determinationalgorithm described above. Since, in some embodiments, the signalindicative of analyte concentration exhibits a pH dependence, in someembodiments, the signal indicative of pH may be used to adjust thesignal indicative of analyte concentration to correct for pH dependence.Thus, in certain such embodiments, the methods further includetransforming the signal indicative of the analyte concentrationutilizing an equation of the form of a modified Michaelis-Mentenequation, such as Equation 1 above, depending on Michaelis-Mentenparameters, such as the parameters “a”, “b”, and “c”, as described aboveas first, second, and third Michaelis-Menten parameters with referenceto Equation 13.

Of course, it is to be understood that when a signal is described hereinas being indicative of one physical quantity, such description is notmeant to necessarily preclude that signal from also being indicative ofanother physical quantity. For instance, a computed analyteconcentration that may be improved through pH correction, was likelycomputed from a signal indicative of analyte concentration whichcontained some pH dependency. Therefore, to a certain extent, such asignal indicative of analyte concentration may also be considered asignal indicative of pH, as will be readily appreciated by one of skillin the art.

The pH dependence of Equation 13 is exhibited through theMichaelis-Menten parameters a_(pH), b_(pH), and c_(pH), as indicated bythe subscript “pH” labeling these parameters. In some embodiments, thepH dependence may need to be determined through a pH calibration. Thus,in certain embodiment methods, the values of one or more of theMichaelis-Menten parameters may be set based on data which includes pHcalibration data and the signal indicative of a pH.

For example, in some embodiment methods, the pH calibration data may begenerated by a pH calibration method. The pH calibration method mayinclude selecting a first test analyte sensing element, and creatingand/or providing a set of at least three solutions of differing knownanalyte concentrations. In certain such embodiments, a first pH isselected (pH1), three solutions of the set of at least three solutionsare adjusted to a pH substantially similar to the selected first pH, anda first set of at least three signals is generated using the first testanalyte sensing element, each signal indicative of the concentration ofanalyte in a different one of the three solutions at the first pH.Measurements are then made at a second pH. Thus, in certain embodiments,a second pH is selected (pH2), three solutions of the set of at leastthree solutions (each of the three may be the same or different than asolution chosen for the first pH) are adjusted to a pH substantiallysimilar to the selected second pH, and a second set of at least threesignals is generated using the first test analyte sensing element, eachsignal indicative of the concentration of analyte in a different one ofthe three solutions at the second pH. Of course, more than threesolutions may be used in either of these steps. And more than two pHsmay also be employed. Generally, the more solutions of differingconcentration and the greater number of different pHs that are employed,the greater the accuracy of the resulting calibration data.

Once the solutions having known analyte concentrations have beenmeasured, and the first and second sets of at least three signals havebeen generated, in some embodiments, the sets of signals are used todetermine (usually approximately) the relationship between one or moreof the Michaelis-Menten parameters and pH. For example, in someembodiments, the pH calibration method may further include computingvalues of each of a first, second, and third Michaelis-Menten parameterat the first pH (a_(pH1), b_(pH1), and c_(pH1)) by an algorithmcomprising fitting a modified Michaelis-Menten equation to a first fitdataset comprising the first set of at least three signals. In certainsuch embodiments, the pH calibration method may further includecomputing values of each of a first, second, and third Michaelis-Mentenparameter at the second pH (a_(pH2), b_(pH2), and c_(pH2)) by analgorithm comprising fitting a modified Michaelis-Menten equation to asecond fit dataset comprising the second set of at least three signals.Thus, in methods such as these, each of the three Michaelis-Mentenparameters has been determined at least two pHs, providing data whichmay be used to create a model of the pH dependence of each of the threeMichaelis-Menten parameters.

To model the pH dependence of the Michaelis-Menten parameters, in someembodiments, the pH calibration method may further include selecting anequation relating the first Michaelis-Menten parameter (a_(pH)) to pH,the equation depending on a first set of pH calibration parameters; andsetting a value for each calibration parameter of the first set ofcalibration parameters based on the value of the first Michaelis-Mentenparameter at the first pH (a_(pH1)) and the value of the firstMichaelis-Menten parameter at the second pH (a_(pH2)). In someembodiments, similar steps are performed with respect to the second andthird Michaelis-Menten parameters (b_(pH) and c_(pH)). Thus, forexample, the pH calibration method may further include selecting anequation relating the second Michaelis-Menten parameter (b_(pH)) to pH,the equation depending on a second set of pH calibration parameters; andsetting a value for each calibration parameter of the second set ofcalibration parameters based on the value of the second Michaelis-Mentenparameter at the first pH (b_(pH1)) and the value of the secondMichaelis-Menten parameter at the second pH (b_(pH2)). Similarly, insome embodiments, the pH calibration method may further includeselecting an equation relating the third Michaelis-Menten parameter(c_(pH)) to pH, the equation depending on a third set of pH calibrationparameters; and setting a value for each calibration parameter of thethird set of calibration parameters based on the value of the thirdMichaelis-Menten parameter at the first pH (c_(pH1)) and the value ofthe third Michaelis-Menten parameter at the second pH (c_(pH2)).

Furthermore, in some embodiments, equations linear in pH may be selectedto relate the first and second Michaelis-Menten parameters to pH, whilea more complicated equation may be selected to relate the thirdMichaelis-Menten parameter to pH. For instance, in some embodiments, thefirst, second, and third Michaelis-Menten parameters may be written as

a _(pH) =a _(7.4) *ρa _(pH) (pH),

b _(pH) =b _(7.4)*ρ_(b) _(pH) (pH), and

c _(pH) =c _(7.4)*ρ_(c) _(pH) (pH)  (Equation 14)

where ρ_(a) _(pH) (pH), ρ_(b) _(pH) (pH), and ρ_(c) _(pH) (pH) are “pHcorrection factors” which approximately account for the pH dependence ofa_(pH), b_(pH), and c_(pH). When the relationship betweenMichaelis-Menten parameter and pH is written as such, eachMichaelis-Menten parameter a_(pH), b_(pH), and c_(pH), is determined bymultiplying the pH 7.4 Michaelis-Menten parameter a_(7.4), b_(7.4), andc_(7.4), by its corresponding “pH correction factor,” ρ_(a) _(pH) (pH),ρ_(b) _(pH) (pH), or ρ_(c) _(pH) (pH), respectively. The pH 7.4Michaelis-Menten parameters may be determined by fitting a modifiedMichaelis-Menten equation to a set of signals indicative of the analyteconcentration of a plurality of solutions of differing analyteconcentrations held at pH 7.4, as described above with respect to, forexample, pH1 and pH2. Alternatively, the parameters a_(7.4), b_(7.4),and c_(7.4) may be supplied by a factory calibration as described inprovisional U.S. patent application No. 61/184,747, “Algorithms forCalibrating an Analyte Sensor,” filed Jun. 5, 2009, which is herebyincorporated herein by reference in its entirety. As yet anotheralternative, a_(7.4), b_(7.4), and c_(7.4) may be determine via aone-point in vivo calibration as also disclosed in the same application.

To determine the “pH correction factors,” ρ_(a) _(pH) (pH), ρ_(b) _(pH)(pH), ρ_(c) _(pH) (pH), some embodiment methods may select a firstequation linear in pH to relate the first Michaelis-Menten parameter topH, and select a second equation linear in pH to relate the secondMichaelis-Menten parameter to pH. In certain such embodiment methods, anequation is selected to relate the third Michaelis-Menten parameter topH which comprises a fraction wherein the numerator is equal to anexponential function of an equation linear in the inverse of pH, and thedenominator is equal to an exponential function of the same linearfunction in the inverse of pH evaluated at pH 7.4. If such equations inpH are selected, then the pH correction factors may be written as

$\begin{matrix}{{{{\rho_{a_{pH}}({pH})} = {{m_{a_{pH}}*{pH}} + \beta_{a_{pH}}}},{{\rho_{b_{pH}}({pH})} = {{m_{b_{pH}}*{pH}} + \beta_{a_{pH}}}},{and}}{{\rho_{c_{pH}}({pH})} = {\frac{^{({\frac{m_{c_{pH}}}{pH} + \beta_{c_{pH}}})}}{^{({\frac{m_{c_{pH}}}{7.4} + \beta_{c_{pH}}})}}.}}} & \left( {{Equation}\mspace{14mu} 15} \right)\end{matrix}$

where the slopes, m_(a) _(pH) , m_(b) _(pH) , m_(c) _(pH) , andintercepts β_(a) _(pH) , β_(b) _(pH) , β_(c) _(pH) , are collectivelyreferred to as pH calibration coefficients (“pHCos”). However, analyticfunctional forms other than linear equations may be chosen to relate thepH correction factors and/or Michaelis-Menten parameters to pH (or toinverses of pH as indicated by Equation 15's expression for ρ_(c) _(pH)(pH)). For instance, in some embodiments, quadratic or higher-orderpolynomials in pH may be appropriate and/or desirable.

In various embodiments, a pH calibration method used to determine valuesof these pHCos may require that values of the Michaelis-Mentenparameters be determined at a second pH (pH2), different than pH 7.4.Values of the parameters at the second pH (a_(pH2), b_(pH2), andc_(pH2)) may be determined by fitting a modified Michaelis-Mentenequation to a set of signals indicative of the analyte concentration ofa plurality of solutions of differing analyte concentrations held at thesecond pH, as described above with respect to, for example, pH1 and pH2.Once this is done, the pH calibration coefficients m_(a) _(pH) and β_(a)_(pH) may be determined by normalizing to a_(7.4) both a_(pH2) anda_(7.4), yielding a_(pH2)/a_(7.4) and 1, and fitting a line to thenormalized values versus the two pHs, pH2 and pH 7.4. The fit may bedetermined using linear least squares or any other method of fitting aline to a set of points. The pH calibration coefficient, m_(a) _(pH) ,is set equal to the slope of the resulting line and the pH calibrationcoefficient, β_(a) _(pH) , is set equal to the intercept. The pHcalibration coefficients m_(b) _(pH) and β_(b) _(pH) may be determinedthe same way from values of b_(pH2) and b_(7.4). Finally, in a manneranalogous to the determination of m_(a) _(pH) , β_(a) _(pH) , m_(b)_(pH) , and β_(b) _(pH) , the pH calibration coefficients m_(c) _(pH) ,and β_(c) _(pH) may be determined from values of c_(pH2) and c_(7.4),however an additional step of linearizing Equation 15's expression forρ_(c) _(pH) (pH) must first be performed. Once the calibration iscomplete, a pH corrected estimated glucose concentration ([Glu]) may becomputed from a fluorescent signal (G_(i)) measured at a particular pH,by using the pHCos (m_(a) _(pH) , β_(a) _(pH) , m_(b) _(pH) , β_(b)_(pH) , m_(c) _(pH) , and β_(c) _(pH) ), the pH 7.4 Michaelis-Mentenparameters (a_(7.4), b_(7.4), and c_(7.4)), and the measured pH (pH) inEquations 14 and 15 to compute a_(pH), b_(pH), and c_(pH), and thenplugging a_(pH), b_(pH), c_(pH) and the measured fluorescent signal(G_(i)) into Equation 13.

Thus, in some embodiments, the first set of pH calibration parameterscomprises the slope and intercept of a first equation linear in pH, andin some embodiments, the second set of pH calibration parameterscomprises the slope and intercept of a second equation linear in pH. Incertain such embodiments, the third set of pH calibration parameters maycomprise the slope and intercept of an equation linear in the inverse ofpH which is related to the third Michaelis-Menten parameter through anexponential function divided by a constant—wherein the constant is equalto the result of evaluating the exponential function of the sameequation linear in the inverse of pH evaluated at a fixed pH level.However, the pH calibration parameters (pHCos) may comprise constantsassociated with analytic functional forms other than linear equationswhich may be suitable and/or desirable. For instance, in someembodiments, the pHCos may include the coefficients of quadratic orhigher-order polynomials in pH.

When measurement devices are mass produced, it may not be feasible orpractical to individually calibrate each measurement device—i.e. useeach individual measurement device to generate individual calibrationdata. It may be more cost effective to select one or more test devicesfrom a batch of mass produced devices, generate calibration data usingthe one or more test devices, and provide that calibration data to eachindividual devices produced in the batch. In some embodiments,variability between measurement devices from the same production batchmay be, to a large extent, attributable to a particular part of themeasurement device. In particular, variability between devices may beattributable to the part of the measurement device which generates asignal indicative of analyte concentration—e.g. the analyte sensingelement—and/or the part of the measurement device that generates asignal indicative of pH—e.g. the pH sensing element. In thesecircumstances, as well as others, it may be advantageous to use acalibration method employing multiple test measurement devices, and/ormultiple test sensing elements, because calibration over multiple testdevices and/or sensing elements may yield more accurate calibration datathan calibration methods which only utilize a single test device and/orsensing element. Accordingly, in some embodiments, the calibrationmethod may further include selecting a second test analyte sensingelement; generating a third set of at least three signals using thesecond test analyte sensing element, each signal indicative of theconcentration of analyte in a different solution of known analyteconcentration at the first pH (pH1); and generating a fourth set of atleast three signals using the second test analyte sensing element, eachsignal indicative of the concentration of analyte in a differentsolution of known analyte concentration at the second pH (pH2).Obviously, calibration methods may similarly employ more than two testdevices, or more particularly, for instance, more than two test analytesensing elements.

In a manner similar to methods utilizing a single test analyte sensingelement, after the solutions having known analyte concentrations havebeen measured and the first, second, third, and fourth sets of at leastthree signals have been generated, in some embodiments, the sets ofsignals are used to determine (usually approximately) the relationshipbetween one or more of the Michaelis-Menten parameters and pH. Forexample, in some embodiments, the pH calibration method may furtherinclude (1) computing values of each of a first, second, and thirdMichaelis-Menten parameter at the first pH (a_(pH1), b_(pH1), andc_(pH1)) by an algorithm comprising fitting a modified Michaelis-Mentenequation to a first fit dataset comprising both the first set of atleast three signals (which was generated with the first test analytesensing element at pH1) and the third set of at least three signals(which was generated with the second test analyte sensing element atpH1); and (2) computing values of each of a first, second, and thirdMichaelis-Menten parameter at the second pH (a_(pH2), b_(pH2), andc_(pH2)) by an algorithm comprising fitting a modified Michaelis-Mentenequation to a second fit dataset comprising both the second set of atleast three signals (which was generated with the first test analytesensing element at pH2) and fourth set of at least three signals (whichwas generated with the second test analyte sensing element at pH2).Essentially, in these types of methods, the signals generated with thesecond test analyte sensing element are used in a combined fit with thesignals generated with the first test analyte sensing element, whichresults in values for each of the first, second, and thirdMichaelis-Menten parameters which take both test analyte sensingelements into account. Alternatively, in some embodiments, a pHcalibration method may take both test analyte sensing elements intoaccount by fitting the signals generated from each test analyte sensingelement separately, and then averaging the results to obtain betterestimates of the Michaelis-Menten parameters. Thus, in some embodiments,the step of computing values of each of a first, second, and thirdMichaelis-Menten parameter at the first pH (a_(pH1), b_(pH1), andc_(pH1)) by an algorithm may further include fitting a modifiedMichaelis-Menten equation to a third fit dataset comprising the thirdset of at least three signals, and averaging the results of fitting thethird fit dataset with the results of fitting the first fit dataset. Inaddition, the step of computing values of each of a first, second, andthird Michaelis-Menten parameter at the second pH (a_(pH2), b_(pH2), andc_(pH2)) by an algorithm may further include fitting a modifiedMichaelis-Menten equation to a fourth fit dataset comprising the fourthset of at least three signals, and averaging the results of fitting thefourth fit dataset with the results of fitting the second fit dataset.

Other methods for estimating analyte concentration which incorporate pHcorrection features and pH calibration steps are also disclosed herein.In some embodiments, these methods are similar to those alreadydescribed above and incorporate similar features, however, additionalfeatures may also be disclosed and, in some embodiments, the disclosedmethods may be more general and described in more general terms. Sincethere are many ways to feasibly implement the discoveries disclosedherein for use in estimating analyte concentration, the followingadditional methods are described in order to illustrate the breadth ofimplementations that are possible.

In some embodiments, for instance, a method of estimating an analyteconcentration from a signal indicative of the analyte concentration mayinclude transforming the signal using an equation of the form of amodified Michaelis-Menten equation wherein the values of one or moreMichaelis-Menten parameters have been adjusted for pH.

In some embodiments, for instance, a method of estimating an analyteconcentration may include generating a signal indicative of the analyteconcentration and generating a signal indicative of a pH, andtransforming the signal indicative of the analyte concentrationutilizing an equation of the form of a modified Michaelis-Mentenequation wherein at least one of the Michaelis-Menten parameters hasbeen substituted with a calibration equation functionally depending on aset of one or more pH calibration parameters and the signal indicativeof pH. One could refer to such an equation as a “substituted” modifiedMichaelis-Menten equation since the Michaelis-Menten parameters havebeen explicitly substituted with equations depending on one or moreother variables—pH and the pH calibration parameters. However, althoughsuch a “substituted” equation exhibits a more complicated analytic form,it nevertheless will still express the basic functional relationships ofthe modified Michaelis-Menten equation.

In some embodiments, the step of transforming the signal indicative ofanalyte concentration may utilize a “substituted” modifiedMichaelis-Menten equation in which each of the first, second, and thirdMichaelis-Menten parameters have been substituted with first, second,and third calibration equations (respectively), each of the equationsdepending on sets of first, second, and third pH calibration parameters(respectively), and each also depending on the signal indicative of pH.In certain embodiments, at least one of the first, second, and thirdcalibration equations is a polynomial in the signal indicative of pH. Incertain such embodiments, each of the first, second, and thirdcalibration equations is a polynomial in the signal indicative of pH. Incertain embodiments, at least one of the first, second, and thirdcalibration equations is a linear equation in the signal indicative ofpH. In certain such embodiments, the first and second calibrationequations are a linear equations in the signal indicative of pH, and thethird calibration equation comprises a fraction wherein the numerator isequal to an exponential function of an equation linear in the inverse ofthe signal indicative of pH, and the denominator is equal to anexponential function of the same linear function in the inverse of thesignal indicative of pH evaluated at fixed pH.

Thus, for example, if each Michaelis-Menten parameter of Equation 13above is assumed to exhibit a linear relationship with pH, then the“substituted” modified Michaelis-Menten equation might appear as

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{\begin{matrix}{\left( {{\chi_{c_{pH},1} \cdot {pH}} + \chi_{c_{pH},0}} \right)*} \\\left\lfloor {G_{i} - \left( {{\chi_{a_{pH},1} \cdot {pH}} + \chi_{a_{pH},0}} \right)} \right\rfloor\end{matrix}}{\begin{matrix}{\left( {{\chi_{a_{pH},1} \cdot {pH}} + \chi_{a_{pH},0}} \right) +} \\{\left( {{\chi_{b_{pH},1} \cdot {pH}} + \chi_{b_{pH},0}} \right) - G_{i}}\end{matrix}}} & \left( {{Equation}\mspace{14mu} 16} \right)\end{matrix}$

and, similarly, if each Michaelis-Menten parameter is assumed to exhibita quadratic relationship with pH then the “substituted” modifiedMichaelis-Menten equation might appear as

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{\begin{matrix}{\left( {{\chi_{c_{pH},2} \cdot {pH}^{2}} + {\chi_{c_{pH},1} \cdot {pH}} + \chi_{c_{pH},0}} \right)*} \\\left\lfloor {G_{i} - \left( {{\chi_{a_{pH},2} \cdot {pH}^{2}} + {\chi_{a_{pH},1} \cdot {pH}} + \chi_{a_{pH},0}} \right)} \right\rfloor\end{matrix}}{\begin{matrix}{\left( {{\chi_{a_{pH},2} \cdot {pH}^{2}} + {\chi_{a_{pH},1} \cdot {pH}} + \chi_{a_{pH},0}} \right) +} \\{\left( {{\chi_{b_{pH},2} \cdot {pH}^{2}} + {\chi_{b_{pH},1} \cdot {pH}} + \chi_{b_{pH},0}} \right) - G_{i}}\end{matrix}}} & \left( {{Equation}\mspace{14mu} 17} \right)\end{matrix}$

where:

-   -   [Glu] is the estimated glucose concentration,    -   χ_(a) _(pH) _(,2), χ_(a) _(pH) _(,1), and χ_(a) _(pH) _(,0) are        polynomial coefficients parameterizing a_(pH)'s dependence on        the pH level,    -   χ_(b) _(pH) _(,2), χ_(b) _(pH) _(,1), and χ_(b) _(pH) _(,0) are        polynomial coefficients parameterizing b_(pH)'s dependence on        the pH level,    -   χ_(c) _(pH) _(,2), χ_(c) _(pH) _(,1), and χ_(c) _(pH) _(,0) are        polynomial coefficients parameterizing c_(pH)'s dependence on        the pH level, and    -   G_(i) is the fluorescent signal (i=1,2), either referenced or        unreferenced, where G₁ is the fluorescence emission at 550 nm        when the fluorophore is excited at 470 nm (which is the        absorption maximum of the fluorophore's base-form), and G₂ is        the fluorescence emission at 550 nm when the fluorophore is        excited at 420 nm (which is the absorption maximum of the        fluorophore's acid-form). Note, however, that other combinations        of excitation and emission wavelengths are also feasible for use        in Equations 16 and 17.

As stated above, although, the “substituted” equations (Equations 16 and17) exhibit a more complicated analytic form, they nevertheless stillexhibit the basic functional relationships of the modifiedMichaelis-Menten equation (Equation 13). In other embodiments, thecalibration equations substituted into the modified Michaelis-Mentenequation may have a functional form other than a polynomial in pH.

Thus, as described above, the calibration equations substituted into themodified Michaelis-Menten equation for the Michaelis-Menten parametersmay take a variety of functional forms and each may have varying numbersof pH calibration parameters. Obviously, more complicated equations mayhave a greater numbers of pH calibration parameters. In any event,depending on the embodiment, various pH calibration methods may be usedto determine the values of the first, second, and third sets of the oneor more pH calibration parameters. In certain such embodiments, each setof pH calibration parameters may be determined by fitting the“substituted” modified Michaelis-Menten equation to a plurality ofsignals, the plurality of signals indicative of analyte concentration ina plurality of solutions at a plurality of pHs. Once values of thevarious pH calibration parameters are determined, pH corrected estimatesof analyte concentrations may be generated from signals indicative ofanalyte concentration and pH.

Example 4

This example concerns the pH calibration of an equilibrium fluorescenceglucose GluCath sensor. Again, the GluCath sensor employs an HPTS-Cys-MAdye operably coupled to a 3,3′-oBBV quencher, with the dye and quencherimmobilized within a hydrogel disposed along the distal region of anoptical fiber, while the proximal end of the optical fiber is coupled toa light source. The pH dependence of this sensor's fluorescence responseto glucose was assumed to approximately follow the modifiedMichaelis-Menten equation labeled as Equation 13 and described above.The Michaelis-Menten a_(pH), b_(pH), and c_(pH) parameters were assumedto bear the relationships to pH set forth in Equations 14 and 15 above.Thus, the a_(pH) and b_(pH), Michaelis-Menten parameters were assumed todepend linearly on pH, while the c_(pH) Michaelis-Menten parameter wasassumed to obey an exponential relationship to the inverse of pH as setforth in Equation 14's expression for c_(pH) and Equation 15'sexpression for ρ_(c) _(pH) (pH). Using this model of the glucosesensor's pH dependence, the pH calibration coefficients, m_(a) _(pH) ,β_(a) _(pH) , m_(b) _(pH) , β_(b) _(pH) , m_(c) _(pH) , and β_(c) _(pH), were determined by the methodology described above in reference toEquations 14 and 15.

Specifically, the effect of pH on the fluorescent signal was determinedexperimentally by measuring the signal at five pH levels (6.8, 7.0, 7.2,7.4, and 7.6) and four glucose concentrations (50 mg/dL, 100 mg/dL, 200mg/dL, and 400 mg/dL). At each pH and glucose level, the stablefluorescent signals G₁ and G₂ were recorded, as displayed in FIG. 22.FIG. 22 illustrates that the data corresponding to a fixed glucoseconcentration of 100 mg/dL exhibits the lowest fluorescent intensity atthe lowest pH (pH 6.8), and the highest fluorescent intensity at thehighest pH (pH 7.6)—and, more generally, that the intensity increasesmonotonically as a function of pH. However, the modulation due toglucose changes inversely with pH—that is, the modulation (the ratio offluorescent intensity at high glucose concentration versus low glucoseconcentration) is lowest at high pH and highest at low pH. Values of thestable fluorescent signal G2 taken from FIG. 22 are replotted in FIG. 23versus glucose concentration—each curve corresponding to a fixed pHlevel. Since the five constant-pH curves in FIG. 23 are generallynon-overlapping, it is clear that changes in pH level have an effect onthe G2 fluorescent signal. From this data, values of theMichaelis-Menten parameters, a_(pH), b_(pH), and c_(pH) (specifically,a_(6.8), a_(7.0), a_(7.4), a₇₃₆, b_(6.8), b_(7.0), b_(7.2), b_(7.4),b_(7.6), c_(6.8), c_(7.0), c_(7.2), c_(7.4), and c_(7.6)), were computedusing Equation 13, see FIG. 24, and normalized to their values at pH7.4, see FIG. 25. FIGS. 24 and 25 illustrate that values of the firstand second Michaelis-Menten parameters, a_(pH) and b_(pH), respectively,vary approximately linearly with pH level, while the value of the thirdMichaelis-Menten parameter, c_(pH), exhibits some degree of non-linearvariation with pH. Hence, Equations 14 and 15 were chosen to modela_(pH), b_(pH), and c_(pH), as described above.

This process for determining values of a_(pH), b_(pH), and c_(pH) wasrepeated over two additional glucose sensors of the same design as thefirst to generate a calibration with improved accuracy. Thus,fluorescent signals were generated with each of the two additionalglucose sensors, at each of the same five pH levels (6.8, 7.0, 7.2, 7.4,and 7.6) and four glucose concentrations (50 mg/dL, 100 mg/dL, 200mg/dL, and 400 mg/dL). This data corresponding to each of the twoadditional glucose sensors was fit with Equations 14 and 15 (as was donewith the initial sensor) in order to generate values of a_(6.8),a_(7.0), a_(7.2), a_(7.4), a_(7.6), b_(6.8), b_(7.0), b_(7.2), b_(7.4),b_(7.6), c_(6.8), c_(7.0), c_(7.2), c_(7.4), and c_(7.6) for eachadditional glucose sensor. The data from the additional two glucosesensors was averaged together with the data from the first sensor togenerate averaged values of the Michaelis-Menten parameters, ā_(6.8),ā_(7.0), ā_(7.2), ā_(7.4), ā_(7.6), b _(6.8), b _(7.0), b _(7.2), b_(7.4), b _(7.6), c _(6.8), c _(7.0), c _(7.2) c _(7.4), and c _(7.6).

Determination of the pH calibration parameters corresponding toEquations 14 and 15 was done using these averaged values. Thus, the pHcalibration parameters corresponding to the “a” Michaelis-Mentenparameter—i.e. m_(a) _(pH) and β_(a) _(pH) —were determined bynormalizing each of the “a” parameters to ā_(7.4), and fitting a line(again using linear least squares) to a plot of these values—i.e.ā_(6.8)/ā_(7.4), ā_(7.0)/ā_(7.4), ā_(7.2)/ā_(7.4), 1, ā_(7.6)/ā_(7.4)versus pH—the slope and intercept being m_(a) _(pH) and β_(a) _(pH) ,respectively. The same was done with the pH calibration parameters m_(b)_(pH) and β_(b) _(pH) , corresponding to the “b” Michaelis-Mentenparameter, and m_(c) _(pH) and β_(c) _(pH) , corresponding to the “c”Michaelis-Menten parameter. The resulting empirically derived values forthese pH calibration coefficients (pHCos) are summarized in Table 5below:

TABLE 5 m_(a) _(pH) = −0.49736 β_(a) _(pH) = 4.6805 m_(b) _(pH) =−0.45178 β_(b) _(pH) = 4.3432 m_(c) _(pH) = 141.06 β_(c) _(pH) =−14.7229

Methods of Estimating Analyte Concentration Incorporating Temperatureand pH Correction

In the preceding disclosure, various methods and/or algorithms aredescribed for correcting a signal indicative of analyte concentration,independently for the effects of temperature, and independently for theeffects of pH. It has also been discovered that various aspects of thesemethods and/or algorithms may be incorporated into combinationalgorithms and/or methods which correct for both the pH and temperaturedependence of signals indicative of analyte concentration. Similarly towhat was discovered with respect to correction for temperature and pHlevel, it has been found that a modified Michaelis-Menten equation canalso be used as an analytical model to take both temperature and pHdependence into account simultaneously. Thus, temperature and pHdependence may be modeled in combination with an equation analogous toEquations 1 and 13 described above:

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{c_{T,{pH}}*\left\lfloor {G_{i} - a_{T,{pH}}} \right\rfloor}{a_{T,{pH}} + b_{T,{pH}} - G_{i}}} & \left( {{Equation}\mspace{14mu} 18} \right)\end{matrix}$

where:

-   -   [Glu] is the estimated glucose concentration,    -   a_(T,pH) is the first Michaelis-Menten parameter “a”, at a        particular temperature and pH,    -   b_(T,pH) is the second Michaelis-Menten parameter “b”, at the        same particular temperature and pH,    -   c_(T,pH) is the third Michaelis-Menten parameter “c”, at the        same particular temperature and pH, and    -   G_(i) is the fluorescent signal (i=1,2), either referenced or        unreferenced, where G₁ is the fluorescence emission at 550 nm        when the fluorophore is excited at 470 nm (which is the        absorption maximum of the fluorophore's base-form), and G₂ is        the fluorescence emission at 550 nm when the fluorophore is        excited at 420 nm (which is the absorption maximum of the        fluorophore's acid-form). Note, however, that other combinations        of excitation and emission wavelengths are also feasible for use        in Equation 18. In the Examples below, G₂ has been used, unless        indicated otherwise.

Accordingly, some embodiment methods of estimating an analyteconcentration include generating a signal indicative of the analyteconcentration, a signal indicative of a temperature, and a signalindicative of a pH. In some embodiments, the signal indicative of theanalyte concentration and the signal indicative of the pH are bothgenerated from a set of at least two signals each of which is indicativeof both the pH and the analyte concentration. For instance, these couldbe the G₁ and G₂ fluorescent signals described above, both of which areindicative of both analyte concentration and pH. In some embodiments,the G₂ fluorescent signal itself may be treated as the signal indicativeof analyte concentration, while G₁ and G₂ are used as signals indicativeof pH, for example, in the pH determination algorithm described above.Furthermore, in some embodiments, the signal indicative of the analyteconcentration, the signal indicative of the temperature, and the signalindicative of the pH are each generated from a set of at least threesignals each of which is indicative of the temperature, the pH, and theanalyte concentration. Since, in some embodiments, the signal indicativeof the analyte concentration exhibits a temperature dependence and a pHdependence which may be quantitatively characterized by a modifiedMichaelis-Menten equation (as described above), methods accomplishingtemperature and pH correction may further include transforming thesignal indicative of the analyte concentration utilizing an equation ofthe form of a modified Michaelis-Menten equation, such as Equation 18above, depending on Michaelis-Menten parameters, such as the parameters“a”, “b”, and “c”, as described above as first, second, and thirdMichaelis-Menten parameters with reference to Equation 18.

The temperature and pH dependence of Equation 18 is exhibited throughthe Michaelis-Menten parameters a_(T,pH), b_(T,pH), and c_(T,pH), asindicated by the subscripts “T” and “pH” labeling these parameters. Insome embodiments, the temperature and pH dependence may need to bedetermined through a calibration method. Thus, in certain embodimentmethods, the values of one or more of the Michaelis-Menten parametersmay be set based on data which includes temperature and pH calibrationparameters, the signal indicative of temperature, and the signalindicative of a pH.

In some embodiment methods, the temperature and pH calibrationparameters may be determined by a calibration method. The calibrationmethod may include selecting a first test analyte sensing element,selecting three differing concentrations of analyte, selecting a firsttemperature (T1) and a second temperature (T2) (the second differingfrom the first), and selecting a first pH (pH1) and a second pH (pH2)(the second differing from the first). Once these selections are made,the calibration method may include computing values of each of a first,second, and third Michaelis-Menten parameter at the selected firsttemperature (T1). This computation may employ an algorithm whichincludes fitting a modified Michaelis-Menten equation to at least threesignals indicative of the selected three differing concentrations ofanalyte in solution at the selected first temperature (T1). The threesignals may be generated, for example, by using the first test analytesensing element to measure the concentration of analyte in each solutionof a set of three solutions, each of which has been prepared so as tocontain one of the three selected concentrations of analyte adjusted tothe first selected temperature (T1).

Calculations are then performed with respect to the selected secondtemperature (T2), analogously to those employed with respect to theselected first temperature (T1). Thus, the calibration method mayinclude computing values of each of a first, second, and thirdMichaelis-Menten parameter at the selected second temperature (T2). Thiscomputation may employ an algorithm which includes fitting a modifiedMichaelis-Menten equation to at least three signals indicative of theselected three differing concentrations of analyte in solution at theselected second temperature (T2). The three signals may be generated,for example, by using the first test analyte sensing element to measurethe concentration of analyte in each solution of a set of threesolutions, each of which has been prepared so as to contain one of thethree selected concentrations of analyte adjusted to the second selectedtemperature (T2).

To account for pH effects, the calibration method may include computingvalues of each of a first, second, and third Michaelis-Menten parameterat the selected first pH level (pH1) and the selected second pH level(pH2). The computation with respect to the selected first pH level (pH1)may employ an algorithm which includes fitting a modifiedMichaelis-Menten equation to at least three signals indicative of theselected three differing concentrations of analyte in solution at theselected first pH level (pH1). The three signals may be generated, forexample, by using the first test analyte sensing element to measure theconcentration of analyte in each solution of a set of three solutions,each of which has been prepared so as to contain one of the threeselected concentrations of analyte adjusted to the first selected pHlevel (pH1). Similarly, the computation with respect to the selectedsecond pH level (pH2) may employ an algorithm which includes fitting amodified Michaelis-Menten equation to at least three signals indicativeof the selected three differing concentrations of analyte in solution atthe selected second pH level (pH2). The three signals may be generated,for example, by using the second test analyte sensing element to measurethe concentration of analyte in each solution of a set of threesolutions, each of which has been prepared so as to contain one of thethree selected concentrations of analyte adjusted to the second selectedpH level (pH2).

Note that though the above described computation uses three selectedanalyte concentrations to compute values of the first, second, and thirdMichaelis-Menten parameters at two temperatures and two pH levels, oneof ordinary skill in the art will readily appreciate that more thanthree selected concentrations may be also be used. Generally, employinggreater numbers of selected analyte concentrations will produce moreaccurate values of the Michaelis-Menten parameters at the varioustemperatures and pH levels. Furthermore, in some embodiments, it may beadvantageous to compute the first, second, and third Michaelis-Mentenparameters at more than two temperatures and more than two pH levels, aswill become apparent to one of ordinary skill in the art from thediscussion that follows.

From values of the first, second, and third Michaelis-Menten parametersat two or more temperatures (a_(T1), b_(T1), c_(T1), a_(T2), b_(T2), andc_(T2)) and two or more pH levels (a_(pH1), b_(pH1), c_(pH1), a_(pH2),b_(pH2), and c_(pH2)), a relationship between each Michaelis-Mentenparameter and temperature and pH may be determined. Thus, in someembodiments, a first calibration equation is selected to relate thefirst Michaelis-Menten parameter to temperature and pH. In someembodiments, the equation may depend on a first set of temperature andpH calibration parameters. In certain such embodiments, a value for eachparameter is set based on the values of the first Michaelis-Mentenparameter at the first temperature (a_(T1)), the second temperature(a_(T2)), the first pH (a_(pH1)), and the second pH (a_(pH2)).Similarly, in some embodiments, a second calibration equation isselected to relate the second Michaelis-Menten parameter to temperatureand pH. In some embodiments, the equation may depend on a second set oftemperature and pH calibration parameters. In certain such embodiments,a value for each parameter is set based on the values of the secondMichaelis-Menten parameter at the first temperature (b_(T1)), the secondtemperature (b_(T2)), the first pH (b_(pH1)), and the second pH(b_(pH2)). Finally, in some embodiments, a third calibration equation isselected to relate the third Michaelis-Menten parameter to temperatureand pH. In some embodiments, the equation may depend on a third set oftemperature and pH calibration parameters. In certain such embodiments,a value for each parameter is set based on the values of the thirdMichaelis-Menten parameter at the first temperature (c_(T1)), the secondtemperature (c_(T2)), the first pH (c_(pH1)), and the second pH(c_(pH2)).

A calibration equation which is selected to relate one of theMichaelis-Menten parameters to temperature and pH may consist of anyfunctional relationship which satisfactorily relates the parameter totemperature and pH once the equation's calibration parameters (if any)are determined. Suitable calibration equations include analyticfunctions such as polynomial functions in temperature and pH. However,the phrase “calibration equation” is used herein to generally denote anyfunctional relationship between one of the Michaelis-Menten parametersand temperature and pH. Thus, for example, a lookup table specifying avalue of any Michaelis-Menten parameter based on particular values oftemperature and pH is considered a “calibration equation” as that phraseis used herein. A set of multiple analytic functions which individuallyapply over particular ranges of temperatures and pHs is also considereda “calibration equation” as that phrase is used herein.

In some calibration methods, the first calibration equation (i.e.selected to relate the first Michaelis-Menten parameter to temperatureand pH) comprises a product of a first pH-independent function and afirst temperature-independent function. One of ordinary skill in the artwill readily appreciate that, in some embodiments, using functions whichsatisfy this criteria may simplify the analysis somewhat, however, sucha person of ordinary skill would also appreciate that such a criteria isnot essential to the operation of the general methods disclosed herein.The same criteria may also apply to the second and third calibrationequations. Thus, in some embodiments, the second calibration equation isthe product of a second pH-independent function and a secondtemperature-independent function, and the third calibration equation isthe product of a third pH-independent function and a thirdtemperature-independent function. In some embodiments, calibrationequations meeting these criteria may be represented by the followingexpression:

a _(T,pH) =a ₀*τ_(a) _(T) (T)*ρ_(a) _(PH) (pH)

b _(T,pH) =b ₀*τ_(b) _(T) (T)*ρ_(b) _(pH) (pH),

c _(T,pH) =b ₀*τ_(c) _(T) (T)*ρ_(c) _(pH) (pH)  (Equation 19)

where:

-   -   τ_(a) _(T) (T), τ_(b) _(T) (T), and τ_(c) _(T) (T) are        “temperature correction factors” which approximately account for        the temperature dependence of a_(T,pH), b_(T,pH), and c_(T,pH);    -   ρ_(a) _(pH) (pH), ρ_(b) _(pH) (pH), and ρ_(c) _(pH) (pH) are “pH        correction factors” which approximately account for the pH        dependence of a_(T,pH), b_(T,pH), and c_(T,pH); and    -   a₀, b₀, c₀ are constants set equal to the value of a_(T,pH),        b_(T,pH), and c_(T,pH) determined at a particular selected        standard temperature and pH level.

When the temperature and pH dependence of each Michaelis-Mentenparameter is expressed in the form of Equation 19, each Michaelis-Mentenparameter, a_(T,pH), b_(T,pH), c_(T,pH), is determined by multiplyingits value at the selected standard temperature and pH level, a₀, b₀, c₀,by its corresponding “temperature correction factor,” τ_(a) _(T) (T),τ_(b) _(T) (T), τ_(c) _(T) (T), and by multiplying again by itscorresponding “pH correction factor,” ρ_(a) _(pH) (pH), ρ_(b) _(pH)(pH), ρ_(c) _(pH) (pH) (of course, the order of multiplication isirrelevant when the temperature and pH dependence are modeled in thismanner). The standard temperature and pH Michaelis-Menten parameters,a_(o), b_(o), c_(o), may be determined by fitting a modifiedMichaelis-Menten equation to a set of signals indicative of the analyteconcentration of a plurality of solutions of differing analyteconcentrations held at the selected standard temperature and pH level.Alternatively, the parameters a₀, b₀, and c₀ may be supplied by afactory calibration as described in provisional U.S. patent applicationNo. 61/184,747, “Algorithms for Calibrating an Analyte Sensor,” filedJun. 5, 2009, which is hereby incorporated herein by reference in itsentirety. As yet another alternative, a₀, b₀, and c₀ may be determinevia a one-point in vivo calibration as also disclosed in the sameapplication.

Furthermore, in some embodiments, the first, second, and thirdpH-independent functions may be selected so as to be linear intemperature; the first and second temperature-independent functions maybe selected so as to be linear in pH; and the thirdtemperature-independent function may be selected to be a fractionwherein the numerator is equal to an exponential function of a thirdfunction linear in the inverse of pH, and the denominator is equal to anexponential function of the same function linear in the inverse of pHevaluated at pH 7.4. Calibration equations satisfying these criteria maybe written as:

$\begin{matrix}{{{\tau_{a_{T}}(T)} = {{m_{a_{T}}*T} + \beta_{a_{T}}}},{{\tau_{b_{T}}(T)} = {{m_{b_{T}}*T} + \beta_{b_{T}}}},{{\tau_{c_{T}}(T)} = {{m_{c_{T}}*T} + \beta_{c_{T}}}},} & \left( {{Equation}\mspace{14mu} 3} \right) \\{{{{\rho_{a_{pH}}({pH})} = {{m_{a_{pH}}*{pH}} + \beta_{a_{pH}}}},{{\rho_{b_{pH}}({pH})} = {{m_{b_{pH}}*{pH}} + \beta_{a_{pH}}}},{and}}{{\rho_{c_{pH}}({pH})} = {\frac{^{({\frac{m_{c_{pH}}}{pH} + \beta_{c_{pH}}})}}{^{({\frac{m_{c_{pH}}}{7.4} + \beta_{c_{pH}}})}}.}}} & \left( {{Equation}\mspace{14mu} 15} \right)\end{matrix}$

These equations, as indicated by their numbering, are identical to theequations discussed above with respect to separate temperaturecalibration and pH calibration. Thus, in methods employing theseequations, the first set of temperature and pH calibration parameterscomprise the slope and intercept of the first pH-independent functionand the slope and intercept of the first temperature independentfunction. Similarly, the second set of temperature and pH calibrationparameters comprise the slope and intercept of the second pH-independentfunction and the slope and intercept of the second temperatureindependent function, and the third set of temperature and pHcalibration parameters comprise the slope and intercept of the thirdpH-independent function and the slope and intercept of the thirdfunction linear in the signal indicative of pH.

Since the calibration equations selected to represent the temperatureand pH correction factors match those separately employed above withrespect to temperature and pH correction, the TempCos (m_(a) _(T) ,β_(a) _(T) , m_(b) _(T) , β_(b) _(T) , m_(c) _(T) , and β_(c) _(T) ) andpHCos (m_(a) _(pH) , β_(a) _(pH) , m_(b) _(pH) , β_(b) _(pH) , m_(c)_(pH) , and β_(c) _(pH) ) determined above separately with respect totemperature and pH may be used in Equation 19, provided that a₀, b₀, andb₀ are determined in a manner consistent with the determination of the37° C. Michaelis-Menten parameters, a₃₇, b₃₇, c₃₇, and the pH 7.4Michaelis-Menten parameters, a_(7.4), b_(7.4), c_(7.4). For instance, ifa₀, b₀, and c₀ are determined at 37° C. and pH 7.4, then these constantsmay be consistently relabeled a_(37,7.4), b_(37,7.4), and c_(37,7.4),and the TempCos and pHCos determined above separately with respect totemperature and pH may be used in Equation 19. Therefore, an expressionfor computing a temperature and pH corrected glucose concentration maybe given by

$\begin{matrix}{\lbrack{Glu}\rbrack = \frac{\begin{matrix}{b_{37.7{.4}}*{\tau_{c_{T}}(T)}*{\rho_{c_{pH}}({pH})}*} \\\left\lfloor {G_{2} - {a_{37,7.4}*{\tau_{a_{T}}(T)}*{\rho_{a_{pH}}({pH})}}} \right\rfloor\end{matrix}}{\begin{matrix}{{a_{37,7.4}*{\tau_{a_{T}}(T)}*{\rho_{a_{pH}}({pH})}} +} \\{{b_{37,7.4}*{\tau_{b_{T}}(T)}*{\rho_{b_{pH}}({pH})}} - G_{2}}\end{matrix}}} & \left( {{Equation}\mspace{14mu} 20} \right)\end{matrix}$

where:

-   -   [Glu] is the estimated glucose concentration,    -   a_(T,pH), b_(T,pH), and c_(T,pH) are the Michaelis-Menten        parameters, at a particular temperature and pH,    -   a_(37,7.4), b_(T,pH), and c_(T,pH) are the Michaelis-Menten        parameters determined at 37° C. and pH 7.4,    -   τ_(a) _(T) (T), τ_(b) _(T) (T), τ_(c) _(T) (T), ρ_(a) _(pH)        (pH), ρ_(b) _(pH) (pH), and ρ_(c) _(pH) (pH) are given by        Equations 3 and 15, and    -   G₂ is the fluorescent emission, either referenced or        unreferenced, at 550 nm when the fluorophore is excited at 420        nm (which is the absorption maximum of the fluorophore's        acid-form). Note, however, that other combinations of excitation        and emission wavelengths are also feasible for use in        Equation 20. In Example 5 below, G₂ has been used.

Example 5

This example concerns the simultaneous temperature and pH calibration ofan equilibrium fluorescence glucose GluCath sensor, and an assessment ofthe accuracy of the calibration by comparison with an independent dataset. Again, the GluCath sensor employs an HPTS-Cys-MA dye operablycoupled to a 3,3′-oBBV quencher, with the dye and quencher immobilizedwithin a hydrogel disposed along the distal region of an optical fiber,while the proximal end of the optical fiber is coupled to a lightsource. The temperature and pH dependence of this sensor's fluorescenceresponse to glucose was assumed to approximately follow Equation20—using the TempCos from Table 2 and the pHCos from Table 5. The 37°C., pH 7.4 Michaelis-Menten parameters, a_(37,7.4), b_(37,7.4),c_(37,7.4), appearing in Equation 20 were determined by averaging dataover multiple sensors derived from fitting a modified Michaelis-Mentenequation to three solutions having known glucose concentrations of 0mg/dL, 100 mg/dL, and 400 mg/dL, followed by a single measurement at 100mg/dL using the individual sensor to adjust the parameters to theindividual sensor.

To test the calibration, measurements were made on two different glucosesolution concentrations (50 mg/dL and 100 mg/dL), at two differenttemperatures (30° C. and 40° C.), and at two different pH levels (pH7.400 and pH 7.035). Reference measurements were made using the YellowSprings Instrument glucose oxidase lab analyzer (“YSI”), the goldstandard of blood glucose measurements. The results are displayed inFIG. 26, FIG. 27 (which displays a zoomed-in portion of FIG. 26), andTable 6 below. In particular, Table 6 lists the predicted glucoseconcentration compared to the YSI reference measurements beforecorrection, and after temperature and pH correction using Equation 20.The mean absolute relative deviation (“MARD”) between the temperatureand pH corrected glucose concentrations and the reference glucoseconcentration was only 5.0%, while the MARD for the same data setwithout temperature and pH correction was 29.6%.

TABLE 6 Uncorrected Temp, pH-corrected Temp pH Glucose GluCath Diff. %Diff. GluCath Diff. % Diff. 40 7.400 100 87.7 −12.3 −12.3% 97.8 −2.2−2.2% 30 7.400 100 133.1 33.1 33.1% 103.7 3.7 3.7% 30 7.035 100 72.2−27.8 −27.8% 93.5 −6.5 −6.5% 40 7.035 100 50.4 −49.6 −49.6% 91.3 −8.7−8.7% 40 7.035 50 25.7 −24.3 −48.7% 46.1 −3.9 −7.8% 30 7.035 50 34.7−15.3 −30.7% 46.4 −3.6 −7.2% 30 7.400 50 63.6 13.6 27.2% 51.5 1.5 2.9%40 7.400 50 46.2 −3.8 −7.7% 50.7 0.7 1.4% MARD 29.6% MARD 5.0%

Other Related Methods of Incorporating Temperature and pH Correction

Other methods for estimating analyte concentration which incorporatetemperature and pH correction features and temperature and pHcalibration steps are also disclosed herein. In some embodiments, thesemethods are similar to those already described above and incorporatesimilar features, however, additional features may also be disclosedand, in some embodiments, the disclosed methods may be more general anddescribed in more general terms. Since there are many ways to feasiblyimplement the discoveries disclosed herein for use in estimating analyteconcentration, the following additional methods are described in orderto illustrate the breadth of implementations that are possible.

In some embodiments, for instance, a method of estimating an analyteconcentration from a signal indicative of the analyte concentration mayinclude transforming the signal using an equation of the form of amodified Michaelis-Menten equation wherein the values of one or moreMichaelis-Menten parameters have been adjusted for temperature and pH.

In some embodiments, for instance, a method of estimating an analyteconcentration of a solution may include generating a signal indicativeof the analyte concentration of the solution, generating a signalindicative of a temperature of the solution, generating a signalindicative of a pH of the solution, and transforming the signalindicative of the analyte concentration utilizing an equation of theform of a modified Michaelis-Menten equation wherein at least one of theMichaelis-Menten parameters has been substituted with a calibrationequation functionally depending on a set of one or more temperature andpH calibration parameters, the signal indicative of the temperature, andthe signal indicative of the pH. One could refer to such an equation asa “substituted” modified Michaelis-Menten equation since theMichaelis-Menten parameters have been explicitly substituted withequations depending on one or more other variables—temperature, pHlevel, and the temperature and pH calibration parameters. However,although such a “substituted” equation exhibits a more complicatedanalytic form, it nevertheless will still express the basic functionalrelationships of the modified Michaelis-Menten equation.

In some embodiments, the step of transforming the signal indicative ofanalyte concentration may utilize a “substituted” modifiedMichaelis-Menten equation in which each of the first, second, and thirdMichaelis-Menten parameters have been substituted with first, second,and third calibration equations (respectively), each of the equationsdepending on sets of first, second, and third temperature and pHcalibration parameters (respectively), and each also depending on thesignal indicative of temperature and the signal indicative of pH.

In certain embodiments, the first calibration equation is the product ofa first pH-independent polynomial in the signal indicative oftemperature and a first temperature-independent polynomial in the signalindicative of pH. Similarly, in certain embodiments, the secondcalibration equation is the product of a second pH-independentpolynomial in the signal indicative of temperature and a secondtemperature-independent polynomial in the signal indicative of pH; andthe third calibration equation is the product of a third pH-independentpolynomial in the signal indicative of temperature and a thirdtemperature-independent function of the signal indicative of pH. Incertain such embodiments, one or more of the first, second, and thirdpH-independent polynomials are linear equations in the signal indicativeof temperature, and one or more of the first and secondtemperature-independent polynomials are linear equations in the signalindicative of pH, while the third temperature-independent function is afraction wherein the numerator is equal to an exponential function of afunction linear in the inverse of the signal indicative of pH, and thedenominator is equal to an exponential function of the same functionlinear in the inverse of the signal indicative of pH evaluated at pH7.4.

Note, that in many if not all of the methods described herein,transforming the signal indicative of analyte concentration using anequation of the form of a modified Michaelis-Menten equation may utilizea look-up table. In some circumstances, function evaluation by use of alook-up table may be more computationally efficient than directapplication of the same function as it is written. To illustrate, afunction mapping a single input variable to a single output variable,e.g. y=ƒ(x), may be evaluated via a look-up table. In this simple case,the look-up table consists of a set of discrete matching input andoutput values, e.g. (x, y) pairs. Evaluating the function ƒ(x) orcomputing the output value y which corresponds to a given input value x,may be accomplished by looking up the input value x in the look-uptable, and choosing the output value y in the table which corresponds toit. If the exact input value does not exist in the look-up table, thecorresponding output value may be determined by interpolating from theoutput values in the table whose corresponding input values are similarto the original input value. Such methodology may be more efficient thanevaluating a function, when looking up values in the look-up table andinterpolating between values when necessary is quicker than applying thefunction as written to a given input value. However, use of a look-uptable should be understood to simply be a potentially efficient way toapproximate the application of a function in analytic form. Accordingly,when transformations using equations are described herein, it should beunderstood that such described transformations encompass the directapplication of the equations as well as the use of a look-up table toapproximate such transformations. More specifically, it is to beunderstood that reference herein to the transformation of one or moresignals using an equation of the form of a modified Michaelis-Mentenequation does encompass transformations utilizing a look-up table.

Thus, as described above, the calibration equations substituted into themodified Michaelis-Menten equation for the Michaelis-Menten parametersmay take a variety of functional forms and each may have varying numbersof temperature and pH calibration parameters. Obviously, morecomplicated equations may have a greater numbers of temperature and pHcalibration parameters. In any event, depending on the embodiment,various temperature and pH calibration methods may be used to determinethe values of the first, second, and third sets of the one or moretemperature and pH calibration parameters. In certain such embodiments,each set of temperature and pH calibration parameters may be determinedby fitting the “substituted” modified Michaelis-Menten equation to aplurality of signals, the plurality of signals indicative of analyteconcentration in a plurality of solutions having differing analyteconcentrations, at a plurality of temperatures, and at a plurality of pHlevels. Once values of the various temperature and pH calibrationparameters are determined, temperature and pH corrected estimates ofanalyte concentrations may be generated from signals indicative ofanalyte concentration, temperature, and pH.

While a number of preferred embodiments of the invention and variationsthereof have been described in detail, other modifications and methodsof using and medical applications for the same will be apparent to thoseof skill in the art. Accordingly, it should be understood that variousapplications, modifications, and substitutions may be made ofequivalents without departing from the spirit of the invention or thescope of the claims.

1-27. (canceled)
 28. A measurement device for estimating glucoseconcentration comprising: an optical sensor comprising a non-enzymatic,equilibrium fluorescence chemical indicator system disposed along adistal region of an optical fiber, the chemical indicator systemcomprising a fluorophore operably coupled to a glucose binding moiety,wherein the fluorophore is configured to generate a fluorescent emissionsignal upon excitation with light, and wherein glucose binding to theglucose binding moiety causes a change in an intensity of thefluorescent emission signal related to the glucose concentration; a pHsensor configured to generate a signal indicative of a pH; and areceiving and processing unit configured to transform the fluorescentemission signal intensity utilizing a first equation for correcting theglucose concentration for changes in pH, wherein the first equation is:${\lbrack{Glu}\rbrack = \frac{c_{pH}*\left\lfloor {G_{i} - a_{pH}} \right\rfloor}{a_{pH} + b_{pH} - G_{i}}},$wherein [Glu] is the estimated glucose concentration. G_(i) is thefluorescent emission signal intensity; a_(pH) is the fluorescentemission signal intensity in the absence of glucose at a particular pH,b_(pH) is the asymptotic signal intensity at infinite glucoseconcentration, minus the fluorescent signal intensity in the absence ofglucose (a_(pH)) at the same particular pH, and c_(pH) is the glucoseconcentration at which the fluorescent signal intensity is one-half ofthe difference between the asymptotic (b_(pH)) and the background(a_(pH)) at the same particular pH; wherein a_(pH), b_(pH), and c_(pH)are set based on data comprising: pH calibration data; and the signalindicative of pH.
 29. The measurement device of claim 28, furthercomprising: a temperature sensor configured to generate a signalindicative of a temperature; wherein the receiving and processing unitis further configured to transform the fluorescent emission signalintensity utilizing a second equation for correcting the glucoseconcentration for changes in pH and temperature, wherein the secondequation is:${\lbrack{Glu}\rbrack = \frac{c_{T,{pH}}*\left\lfloor {G_{i} - a_{T,{pH}}} \right\rfloor}{a_{T,{pH}} + b_{T,{pH}} - G_{i}}},$wherein a_(T,pH) is the fluorescent emission signal intensity in theabsence of glucose at a particular pH and temperature, b_(T,pH) is theasymptotic signal intensity at infinite glucose concentration, minus thefluorescent signal intensity in the absence of glucose (a_(T,pH)) at thesame particular pH and temperature, and c_(T,pH) is the glucoseconcentration at which the fluorescent signal intensity is one-half ofthe difference between the asymptotic (b_(T,pH)) and the background(a_(T,pH)) at the same particular pH and temperature; wherein a_(T,pH),b_(T,pH), and b_(T,pH) are set based on data comprising: temperaturedata; and the signal indicative of temperature.
 30. The measurementdevice of claim 28, wherein the optical sensor further comprises: atleast one light source configured to generate light; and at least onedetector configured to detect the fluorescent emission signal intensityand generate a signal indicative of the glucose concentration. 31.(canceled)
 32. (canceled)
 33. (canceled)
 34. The measurement device ofclaim 28, wherein the indicator system further comprises an immobilizingmedium configured to prevent the fluorophore and/or the binding moietyfrom diffusing out of the sensor.
 35. The measurement device of claim29, wherein the temperature sensor and the optical sensor are co-locatedalong the distal region of the optical fiber.
 36. The measurement deviceof claim 29, wherein the optical sensor further comprises: at least onelight source configured to generate light; and at least one detectorconfigured to detect the fluorescent emission signal intensity andgenerate a signal indicative of the glucose concentration.
 37. Themeasurement device of claim 29, wherein the indicator system furthercomprises an immobilizing medium configured to prevent the fluorophoreand/or the binding moiety from diffusing out of the sensor.
 38. Themeasurement device claim 28, wherein the fluorophore is HPTS-triCys-MA.39. The measurement device claim 28, wherein the glucose binding moietycomprises boronic acid.
 40. The measurement device of claim 28, whereina_(pH), is defined by the equation a_(pH)=a_(7.4)*ρ_(a) _(pH) (pH),wherein b_(pH) is defined by the equation b_(pH)=b_(7.4)*ρ_(b) _(pH)(pH), and wherein c_(pH) is defined by the equation c_(pH)=c_(7.4)*ρ_(c)_(pH) (pH).
 41. The measurement device of claim 29, wherein a_(T,pH) isdefined by the equation a_(T,pH)=a₀*τ_(a) _(T) (T)*ρ_(a) _(pH) (pH),wherein b_(T,pH) is defined by the equation b_(T,pH)=b₀*τ_(b) _(T)(T)*ρ_(b) _(pH) (pH), and wherein c_(T,pH) is defined by the equationc_(T,pH)=b₀*τ_(c) _(T) (T)*ρ_(c) _(pH) (pH).